President Isaac Herzog of Israel used an address to Congress on Wednesday to try to smooth over fresh tensions between his country and the United States, appealing to American lawmakers to continue investing in the “irreplaceable” relationship even as he acknowledged problems at home that have strained that bond.

Mr. Herzog kept his words strictly nonpartisan as he spoke about the strength of the security partnership between the United States and Israel, decried Iran’s nuclear ambitions and thanked the United States for shepherding through the Abraham Accords, which he called a “game changer” for peace in the Middle East. And he elicited applause from both Republicans and Democrats as he lauded the vibrancy of Israel’s democracy and recalled the 75-year alliance with the United States.

“We are proud to be the United States’s closest partner and friend,” Mr. Herzog told lawmakers. “When the United States is strong, Israel is stronger. And when Israel is strong, the United States is more secure.”

The speech was an effort to solidify bipartisan support for Israel at a time when a growing number of Democrats have questioned Prime Minister Benjamin Netanyahu’s embrace of right-wing policies they see as undemocratic, and an emboldened left wing is openly accusing the country of imposing apartheid policies against Palestinians. It also appeared aimed at reassuring Israelis, who have taken to the streets by the thousands to protest Mr. Netanyahu’s policies, that the country still values its democratic, pluralistic legacy.

Israel “takes pride in its vibrant democracy, its protection of minorities, human rights and civil liberties, as laid down by its parliament, the Knesset, and safeguarded by its strong Supreme Court and independent judiciary,” Mr. Herzog said. He later added that the debates roiling the Israeli population were “the clearest tribute to the fortitude of Israel’s democracy.”

The reception for Mr. Herzog in the packed House chamber was staunchly supportive, with frequent standing ovations by the assembled lawmakers, including when he decried Palestinians for destroying the prospects for peace by supporting terror attacks against Israel.

“Israel cannot and will not tolerate terror, and we know that in this we are joined by the United States of America,” Mr. Herzog said.

But the camaraderie within the House chamber on Wednesday masked a fraught debate over Israel’s policies raging just outside its doors, where a group of left-wing House Democrats who boycotted the speech have accused Israeli leaders of endorsing racist policies against Palestinians that have led to a system of apartheid.

On the eve of the speech, 10 left-wing House Democrats declined to vote for a widely backed resolution stating that Israel was neither racist nor an apartheid state, alongside declarations of strong support for Israel and a denouncement of antisemitism and xenophobia in all its forms. Republicans had written the resolution after Representative Pramila Jayapal, Democrat of Washington and a leading progressive, told a liberal audience over the weekend that Israel “is a racist state.”

Though Ms. Jayapal later walked back the comments — and voted for the resolution — the episode touched off a bitter standoff in Congress, as Republicans accused Democrats of tolerating antisemitism and Democrats charged that Republicans were trying to turn Israel into a partisan issue by driving a wedge among their members.

Mr. Herzog acknowledged the tensions only glancingly in his speech.

“I respect criticism, especially from friends, although one does not always have to accept it,” Mr. Herzog said. “But criticism of Israel must not cross the line into negation of the state of Israel’s right to exist.” He said that was “not legitimate diplomacy, it is antisemitism” — a line met in the chamber with thunderous applause.

None of the lawmakers criticizing Israel’s policies as apartheid this week questioned Israel’s right to exist. Instead, they cited the findings of various human rights organizations, including Amnesty International, Human Rights Watch and a United Nations report, that have said that Israel’s unequal treatment of Jews and Palestinians under law, as well as its pursuit of settlement construction in the West Bank in violation of international law, amounts to apartheid.

“The facts are clear, and the international consensus is resounding — Israel is an apartheid state,” Representatives Rashida Tlaib of Michigan and Cori Bush of Missouri, two of the Democrats who boycotted Mr. Herzog’s speech, said in a joint statement. They said it was “shameful to deliberately ignore — and even normalize — this racist and oppressive system of apartheid.”

Ms. Tlaib and Ms. Bush were joined by Democratic Representatives Jamaal Bowman and Alexandria Ocasio-Cortez, both of New York; André Carson of Indiana; Summer Lee of Pennsylvania; Ilhan Omar of Minnesota; Ayanna S. Pressley of Massachusetts; and Delia Ramirez of Illinois, in voting against the resolution. Representative Betty McCollum, Democrat of Minnesota, voted “present,” declining to register a position.

Though Ms. Jayapal voted in favor of the resolution, she joined several of those members in skipping Mr. Herzog’s speech on Wednesday, as did Representative Nydia M. Velázquez, Democrat of New York, who said the current Israeli government was “undermining” the right to self-determination for all people and diminishing the likelihood of a two-state solution for Israelis and Palestinians.

As a result, there was no hint of dissent in the chamber when Mr. Herzog stated that the United States and Israel “have always stood for the same values.”

“Our two nations are both diverse, life-affirming societies that stand for liberty, equality and freedom,” Mr. Herzog said. “Both peoples seek to repair the cracks in our world.”

Lawmakers also demonstrated their approval and sympathy when Mr. Herzog paid tribute to Israeli citizens who disagree with the government’s policies, particularly proposals seeking to weaken the national court system and centralize power.

Several Democratic lawmakers, as well as President Biden, have expressed concerns in recent months about Mr. Netanyahu’s embrace of the measures, and Mr. Herzog has previously warned the backlash could pitch the country into a civil war. On Wednesday, he appealed to lawmakers — and Israelis — to see that debate playing out on the streets as democracy in action.

“Our democracy is also reflected in the protesters taking to the streets all across the country, to emphatically raise their voices and fervently demonstrate their point of view,” he said. “Although we are working through sore issues, just like you, I know our democracy is strong and resilient.”

Israel’s national security adviser, Tzachi Hanegbi, announced late Wednesday that the country would allow American citizens of Palestinian origin to visit starting on Thursday. The move will allow them to transit through Israel on their way to and from the occupied territories. Currently, Palestinian Americans visiting the West Bank and Gaza must make a lengthier and more arduous journey via Jordan or Egypt.

If the plan is carried out to the satisfaction of American officials, the U.S. government is expected to waive visa requirements for Israeli citizens in a reciprocal gesture. Matthew Miller, the State Department spokesman, told reporters on Wednesday that Israel’s changes would “ensure equal treatment to all U.S. citizen travelers without regard to national origin, religion or ethnicity,” and that the U.S. would make a decision about admitting Israel to its visa waiver program by Sept. 30.

On Capitol Hill, Mr. Herzog received a warm reception from members of both parties, who had jointly invited him to address Congress and met with him together on Wednesday before his speech. He was the ninth Israeli leader to address Congress, and the first to do so since 2015, when Mr. Netanyahu delivered an address at the invitation of Republicans over President Obama’s objections and used it to slam the nuclear deal his administration was trying to negotiate with Iran. Only one other Israeli president — Mr. Herzog’s father, Chaim Herzog — has addressed Congress, in 1987.

Mr. Herzog took a noticeably more conciliatory tone than Mr. Netanyahu, even when talking about Iran’s nuclear ambitions.

“Allowing Iran to become a nuclear threshold state — whether by omission or diplomatic commission — is unacceptable,” he said, adding that “the world cannot remain indifferent to the Iranian regime’s call to wipe Israel off the map.”

Mr. Herzog made no specific mention of the informal agreement that the Biden administration has been trying to strike with Tehran to limit its nuclear program, through which it has been building a stockpile of highly enriched uranium but has not yet attempted to build a bomb.

In fact the only moment of the speech that appeared to inspire any division at all was when Mr. Herzog mentioned that Tel Aviv hosts “one of the largest and most impressive L.G.B.T.Q. Pride Parades in the world,” a line that inspired cheers from Democrats, but silence from most Republicans. It was a reminder that the two parties are warring over a G.O.P. drive to impose conservative social policies throughout the government.

Michael Crowley contributed reporting from Washington and Patrick Kingsley from Jerusalem.