Republican efforts to restrict gender-transitioning treatment hit roadblocks in three states on Wednesday. Kansas lawmakers failed to override the Democratic governor’s veto of a bill that would have banned the care for minors, the Justice Department sued Tennessee over its new ban and a Missouri judge temporarily blocked the enforcement of an emergency rule that would have restricted treatment for transgender children and adults.

Across the country, transgender rights have emerged this year as a defining legislative issue, with Republicans enacting sweeping new restrictions in states they control. At least 11 states have passed laws or policies in recent months that ban or significantly limit the use of puberty blockers, cross-sex hormones and transition surgery for people under 18.

In just the past few weeks, new bans have been signed into law in Idaho, Indiana and North Dakota, with similar policies still under consideration in other states.

But a vote in the Kansas Senate on Wednesday kept in place Gov. Laura Kelly’s veto of a bill that would have revoked the medical licenses of doctors who provided gender-transitioning care to children and allowed people who received that treatment as children to sue their doctors. In Missouri, a state judge blocked new restrictions, which were set to take effect on Thursday, until at least Monday evening.

And in Tennessee, the Justice Department filed a lawsuit asserting that a ban on gender-transitioning care for minors signed into law this year by Gov. Bill Lee, a Republican, violated the Equal Protection Clause of the 14th Amendment.

“The right to consider your health and medically approved treatment options with your family and doctors is a right that everyone should have, including transgender children, who are especially vulnerable to serious risks of depression, anxiety and suicide,” Assistant Attorney General Kristen Clarke, of the Civil Rights Division of the Justice Department, said in a statement.

Mr. Lee called the lawsuit “federal overreach at its worst” and said the state would defend the law in court.

As Republicans have pushed through new restrictions on transgender rights, including prohibiting access to bathrooms and sports teams, they have argued that the measures protect children from making life-altering medical decisions they may later regret.

“Sometimes, unfortunately, we as a Legislature have to be the last line of defense when parents have lost their way, when a health care system has lost its way,” said State Senator Mark Steffen, a Kansas Republican.

But L.G.B.T.Q. rights groups have criticized the policies as bigoted attacks that go against best medical practices.

Major medical organizations, including the American Academy of Pediatrics, support gender-transitioning care and have said that bans pose serious mental health risks to young people, infringing not only on their rights but also on the rights of doctors and parents.

Even as the Kansas Legislature, where Republicans hold supermajorities, failed to override Ms. Kelly’s veto of the ban on gender-transitioning care, both chambers voted to override her objections on another bill that, among other things, would require jails to have separate facilities for inmates based on their sex assigned at birth.

Though most of the changes nationally have come through legislation, Attorney General Andrew Bailey of Missouri sought to use his state’s consumer protection law to restrict transition treatments. Mr. Bailey’s emergency rule was set to take effect on Thursday and to remain in place until Feb. 6, 2024. Unlike many other attempts this year to limit gender-transitioning treatments, Mr. Bailey’s restrictions would have applied to adults as well as minors.

Mr. Bailey, who was appointed to his position in January and is seeking election to a full term, said in announcing the rule this month that substantial guardrails were needed around transition care because of what he described as insufficient medical literature on their long-term effects and risks.

The attorney general’s rule did not seek to ban transition care, but it imposed limits, including at least 18 months of therapy with a psychologist or psychiatrist before new patients could receive puberty-blocking drugs or surgeries.

After hearing arguments on the rule on Wednesday afternoon, a state judge delayed enforcement until at least Monday evening. The judge, Ellen H. Ribaudo of St. Louis County Circuit Court, said she needed more time to review briefings and planned to rule by Monday on a request by L.G.B.T.Q. advocacy groups for a temporary restraining order.

Emily Cochrane contributed reporting.