The Biden administration, which has been under pressure for its support of Israel’s war in Gaza, will not withhold military aid from a troubled military unit accused of human rights violations in the West Bank, so long as Israel continues with steps to hold the members of the unit accountable.

In an undated letter, Secretary of State Antony J. Blinken told the House speaker, Mike Johnson, that the United States was working with Israel to address charges against the unit, the Netzah Yehuda battalion. Though the letter did not mention the battalion’s name, a U.S. official confirmed that Mr. Blinken was referring to Netzah Yehuda, which has been investigated for crimes in the West Bank predating the Oct. 7 Hamas-led attack that set off the war in Gaza.

The official, speaking on the condition of anonymity to discuss delicate diplomacy, said that the Biden administration could still take action against Netzah Yehuda if it concludes that Israel has not taken sufficient steps to hold its members to account.

The letter, obtained by The New York Times, said the State Department had determined that Netzah Yehuda had committed “gross human rights violations” against Palestinians in the Israeli-occupied West Bank.

U.S. officials had reached similar findings about two other Israeli military units and two civilian units, the letter said, but in those cases the Biden administration had decided not to withhold military aid because Israel was already acting to “bring to justice” culpable service members.

Mr. Blinken assured Mr. Johnson in the letter, reported earlier by ABC News, that the United States “will not delay the delivery of any U.S. assistance, and Israel will be able to receive the full amount appropriated by Congress.”

Under federal statutes commonly known as the Leahy law, the U.S. government must deny aid to foreign military units found to have committed gross violations of human rights without accountability. The law allows for the targeting of individual units without cutting off entire foreign militaries.

It was not clear what practical effect any such move might have, given that funding of specific Israeli units is hard to track, and it is unclear whether the units mentioned in the letter receive American training or equipment.

Still, the news last week that U.S. officials were considering withholding aid from Israeli military units for abuses prompted a furious response from Israel and from Mr. Johnson, a strong supporter of the current Israeli government. Mr. Johnson said this week that he had called the White House in protest and had received an assurance in writing that none of the billions in additional U.S. aid to Israel approved by Congress this week would be affected.

The Biden administration has faced growing calls to restrict American aid to Israel over its military offensive in Gaza in response to the Hamas-led attacks in October. President Biden so far has declined to place conditions on U.S. aid over Israel’s devastating tactics in the Gaza war, though he has taken several steps in response to violence by Israelis in the West Bank, including placing sanctions against several Israeli settlers for what the U.S. has called “extremist” acts of violence against Palestinians.

In his letter to the Republican House speaker, Mr. Blinken said that two Israeli battalions and “civilian authority units,” none of which he named, had committed human rights abuses but that he had “determined that the Israeli government has conducted effective remediation of the units involved.” He defined remediation as a process in which a foreign government takes “effective steps to bring to justice the responsible members of the unit.”

In the case of Netzah Yehuda, which he did not cite by name, he said that “there has not been effective remediation to date” but that the Israeli government “has presented new information regarding the status of the unit, and we will engage on identifying a path to effective remediation for this unit.”

Mr. Blinken is planning to travel to Israel next week for meetings with Israeli leaders to discuss efforts to free hostages from Gaza and an impending Israeli military operation in the southern Gaza city of Rafah, an Israeli official said on Friday. It was not immediately clear whether he would discuss Netzah Yehuda. Mr. Blinken has discussed the matter by phone with senior Israeli officials in recent days.

Under the terms of a 10-year security agreement that the United States and Israel reached in 2016, the United States must consult with Israeli officials before placing restrictions on security assistance. That consultation is ongoing, according to the U.S. official.

Netzah Yehuda, which was created to accommodate the religious practices of Israel’s ultra-Orthodox community, has been repeatedly accused of mistreating Palestinians.

In January 2022, according to witnesses, its soldiers bound and gagged a 78-year-old Palestinian American who died of a heart attack while in military custody. An investigation concluded that the two soldiers who bound the man thought he was sleeping. The soldiers faced disciplinary action but no criminal charges were brought.

The unit was transferred in 2022 from the West Bank to the Golan Heights in northern Israel, according to Mr. Blinken’s letter.

Mr. Blinken added that no other Israeli units had been found culpable of rights violations under the Leahy Law and that the administration’s deliberations “will have no impact on our support for Israel’s ability to defend itself against Hamas, Iran, Hezbollah or other threats.”