An Israeli researcher missing for months in Iraq is being held by a Shiite militia, according to a statement from the office of Prime Minister Benjamin Netanyahu.

Elizabeth Tsurkov, 36, a doctoral student at Princeton University, was kidnapped and held by the group Kataib Hezbollah, an Iraqi militia linked to Iran, after leaving a cafe in Baghdad, the Iraqi capital, in late March, according to her family and people with knowledge of her case.

She holds both Israeli and Russian passports and entered the country using her Russian passport, according to the Israeli government. Israel and Iraq do not have diplomatic relations, so she would not have been allowed to enter with an Israeli passport.

Ms. Tsurkov went to Iraq in January to do academic research. As well as studying at Princeton, she is a fellow at the New Lines Institute for Strategy and Policy, a Washington-based research group.

“Elizabeth Tsurkov is still alive and we hold Iraq responsible for her safety and well-being,” the Israeli prime minister’s office said in the statement. “She is an academic who visited Iraq on her Russian passport, at her own initiative pursuant to work on her doctorate and academic research on behalf of Princeton University in the U.S. The matter is being handled by the relevant parties in the State of Israel out of concern for Elizabeth Tsurkov’s security and well-being.”

Ms. Tsurkov’s family confirmed in a statement that she had been kidnapped while doing research for her Ph.D. dissertation at Princeton.

“She was kidnapped in the middle of Baghdad, and we see the Iraqi government as directly responsible for her safety,” the family’s statement said. “We ask for her immediate release from this unlawful detention.”

The Iraqi government had no immediate response.

The kidnapping spotlighted a problem that Iraq’s leaders have been grappling with: Some military groups absorbed into Iraq’s security forces have stronger ties to Iran than to Iraq, and security officials say Kataib Hezbollah is the most prominent.

The seizure of Ms. Tsurkov raised fears that she could be transferred to Iran, but there has been no indication that that has happened, according to the people familiar with the episode.

A fluent Arabic speaker, Ms. Tsurkov is an experienced analyst and commentator on the Middle East. If her abduction turns out to be linked more directly to Iran, it would be a serious escalation in a long-running shadow war between Israel, Iran and Iranian proxies across the Middle East.

Kataib Hezbollah is a separate organization from the Iran-backed Hezbollah movement in Lebanon, and is tightly linked to Iran’s powerful Islamic Revolutionary Guards Corps. It is listed by the U.S. government as a terrorist organization and was accused of firing rockets in 2019 on an Iraqi air base in an attack that killed an American contractor.

That attack contributed to the U.S. decision to carry out a targeted killing of Qassim Suleimani, who headed Iran’s Quds Force, the overseas arm of the Revolutionary Guards.

Kataib Hezbollah has repeatedly attacked U.S. Army posts in Iraq and Syria over the past 20 years. On Dec. 31, 2019, the group spearheaded an attack on the American Embassy in Baghdad, setting fire to its gates and breaking into the main checkpoint but stopping short of breaching the inner compound.

The siege went on for almost three days, and on Jan. 3, 2020, the United States killed Mr. Suleimani. He was accused of being behind the assault on the embassy as well as being responsible for the deaths of hundreds of U.S. service members across the Middle East.

The U.S. State Department said in a statement on Wednesday: “We are aware of this kidnapping and condemn the abduction of private citizens. We defer to Iraqi authorities for comment.”

Ms. Tsurkov was kidnapped earlier this year as she was returning to her home in Baghdad after leaving the Ridha Alwan cafe in Karada, a neighborhood known for its relaxed atmosphere, according to the people briefed on the events. Full of coffee shops, clothing stores and markets, it is an area frequented by Westerners and is one of the most religiously mixed in Baghdad, with a number of Christian churches as well as mosques.

She had undergone emergency back surgery in Baghdad and was recovering from the operation before she was kidnapped. She had been active on social media, tweeting regularly about issues in the Middle East. Her last post was on March 21; it linked to a paper she had published on Syria for The New Lines Institute.

Ms. Tsurkov has worked across the Middle East for more than a decade and had visited Iraq more than 10 times, according to Iraqi officials. Her research centers on societies in conflict and post-conflict situations in the Middle East, with a particular focus on Syria and Iraq.

Born in 1986 in St. Petersburg, Russia, she is the daughter of political dissidents who were jailed by the Soviet authorities after working alongside Natan Sharansky, a prominent activist who campaigned for Soviet Jews to be allowed to emigrate to Israel. Ms. Tsurkov is mentioned in passing in Mr. Sharansky’s memoir, “Fear No Evil,” though not by name, in a passage about her parents.

Like Mr. Sharansky, the family eventually emigrated to Israel. Ms. Tsurkov arrived with her mother and sister in 1990, the year before her father. The family later moved to an Israeli settlement in the occupied West Bank.

During her mandatory Israeli military service, Ms. Tsurkov grew more interested in the Arab world, according to a biographical podcast interview she gave that was released in 2021.

She later earned a bachelor’s degree in international relations at the Hebrew University in Jerusalem, and master’s degrees in Middle Eastern studies at Tel Aviv University and in political science at the University of Chicago.

She lives in Istanbul, according to her website.

Ronen Bergman reported from Tel Aviv; Patrick Kingsley from Jerusalem; Alissa J. Rubin from Baghdad; and Adam Goldman from Washington. Falih Hassan contributed reporting from Baghdad.