JERUSALEM — A day after barring Representative Rashida Tlaib under pressure from President Trump, Israel said on Friday that she could visit her 90-year-old grandmother, who lives in the occupied West Bank, but only after she agreed in writing not to “promote boycotts against Israel” during her trip.

But after being criticized by backers of a boycott, Ms. Tlaib, too, reversed course on Friday, saying that she would not make the trip, after all. “Visiting my grandmother under these oppressive conditions stands against everything I believe in,” she wrote on Twitter.

“Silencing me & treating me like a criminal is not what she wants for me,” Ms. Tlaib said of her grandmother. “It would kill a piece of me.”

The announcement from Israel appeared to be a second shift in position by the government of Prime Minister Benjamin Netanyahu. The Israeli Interior Ministry initially approved a planned official visit by Ms. Tlaib, of Michigan, and another Democratic lawmaker, Representative Ilhan Omar of Minnesota. But after a public objection by President Trump, it blocked them, citing their support for the anti-Israel Boycott, Divestment and Sanctions movement.

Ms. Tlaib had written to the Israeli interior minister, Aryeh Deri, appealing to be allowed to see her relatives, particularly her 90-year-old grandmother, who lives in Beit Ur al-Fouqa, a Palestinian village west of Ramallah.

“This could be my last opportunity to see her,” Ms. Tlaib wrote on congressional letterhead. “I will respect any restrictions and will not promote boycotts against Israel during my visit.”

“In light of that,” Mr. Deri’s office said on Friday, the minister decided to allow her into Israel and “expressed hope that she would keep her commitment and that the visit would truly be solely for humanitarian purposes.”

The developments raised new questions about how the back-and-forth would ultimately affect politics in both countries; their relationship has become a divisive campaign issue in both the Sept. 17 election in Israel and the 2020 presidential race in the United States.

In Israel, Mr. Netanyahu’s acquiescence to Mr. Trump on Thursday provided instant fodder to rivals and critics who have long warned that the president’s showering the prime minister with political gifts would eventually come at a price.

Mr. Netanyahu’s allies on the right generally approved of his decision, saying Israel owed its adversaries nothing, regardless of their prominence or high office.

On the Israeli left and among some Palestinians, Ms. Tlaib’s quick acceptance of Israel’s conditions for a personal visit raised concerns that she had unwittingly set back the cause of critics of the Israeli occupation.

“What is truly upsetting is that @RashidaTlaib fell in this trap and accepted to demean herself and grovel,” Nour Odeh, a political analyst based in Ramallah and a former Palestinian Authority spokeswoman, wrote on Twitter.

Beyond mere appearances, if Ms. Tlaib had held to her promise to refrain from promoting boycotts, it could have been a setback for opponents of an Israeli law that allows the country to shut its doors to foreign supporters of the boycott campaign.

When Israel tried last year to use that law to bar an American student, Lara Alqasem, from studying in Jerusalem because she had belonged to a group that supports B.D.S., Israeli officials tried to get her to renounce the campaign and promise not to promote it while in the country.

She refused to buckle, despite spending weeks in jail, and instead took the case to the Israeli Supreme Court. Ultimately, Ms. Alqasemwas granted a visa that allows the country to eject her if she promotes B.D.S., but she made no promises not to do so, said her lawyer, Leora Bechor.

Ms. Bechor warned that Ms. Tlaib, by promising not to promote boycotts while she is in Israel, had very likely given Israel ammunition with which to demand similar commitments from ordinary Americans who support a boycott of Israel — even those who are married to Israelis or Palestinians and live in the country or on the West Bank.

“She’s creating a situation where families who are not here for a one-week visit, but are living here permanently, are not going to be able to enter unless they renounce all of their activities,” said Ms. Bechor, who said she handles many family reunification cases. “Israel will take advantage of this and say, `If you don’t renounce, you can’t live here anymore.’ ”

Ms. Tlaib and Ms. Omar, along with Stacey Plaskett, the nonvoting congressional representative of the United States Virgin Islands, had planned a four-day fact-finding tour to examine the condition of Palestinians under Israel occupation. The three women, all Democrats, had intended to focus on the effects of a number of policy moves by the Trump administration, including aid cuts to East Jerusalem hospitals and Palestinian refugees, and the move of the United States embassy to Jerusalem.

Though Israel’s ambassador in Washington, Ron Dermer, said in July that Israel would not bar any member of Congress, the news site Axios reported last week that Mr. Trump had privately lobbied Mr. Netanyahu to bar Ms. Tlaib and Ms. Omar. An Israeli official said a call came from the Trump administration as late as this week pressing Mr. Netanyahu to do so.

Then, Thursday morning, Mr. Trump said on Twitter that Israel’s admitting the two Democratic congresswomen “would show great weakness.”

Ms. Tlaib and Ms. Omar, the first two Muslim women elected to Congress, are vocal critics of the president. Mr. Trump has vilified them, seeking to portray them as the new face of the Democratic Party.

The pressure from the White House forced Mr. Netanyahu to choose between ignoring Mr. Trump or angering Democratic leaders in Congress, who urged him to allow the visit to take place despite their differences with Ms. Tlaib and Ms. Omar on policy toward Israel.

When he finally explained his decision, Mr. Netanyahu argued that the trip itinerary was one-sided and that its “sole objective is to strengthen the boycott against us and deny Israel’s legitimacy.”

But in announcing the ban on their official trip under a law that allows Israel to bar those who take a leading role in advancing boycotts of the country, Mr. Deri, the interior minister, also left open the door to admitting Ms. Tlaib for a personal visit. If her request “for humanitarian reasons is submitted for a private meeting with her family, subject to the appropriate obligations, he will consider it,” his office said on Thursday.

Mr. Trump’s intervention, urging another country to act against his domestic critics, was the latest example of his willingness to violate the norms of conduct by an American president.

Ms. Omar and Ms. Tlaib make up half of what has been dubbed “the Squad,” outspoken leftist Democrats who were first elected last November. The others in the group are Representatives Alexandria Ocasio-Cortez of New York and Ayanna S. Pressley of Massachusetts.

Mr. Trump and other Republicans have characterized them as anti-American extremists, and as the face of the Democratic Party — although, as first-term lawmakers, they wield little power. The president last month told them to “go back” to their home countries, though they are American citizens and all but Ms. Omar were born in the United States.

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