The White House is again considering setting the number of refugees who can enter the United States through September at about 62,500, according to three people familiar with the deliberations, under pressure from immigrant rights groups furious about President Biden’s recent retreat from that target.

Less than two weeks after White House press secretary Jen Psaki said Biden intends to announce a new cap for the fiscal year by May 15, but signaled that his original target was no longer realistic, people inside and outside the White House suddenly sound hopeful about landing at or near the number the Biden administration announced with some fanfare in February.

“The United States must reject the previous administration’s cruel legacy of anti-refugee policies and return to our longstanding bipartisan tradition of providing safety to the world’s most vulnerable refugees,” the senators, led by Senate Judiciary Committee Chairman Richard J. Durbin (D-Ill.) wrote in the letter, which was sent to the White House on Tuesday afternoon and obtained by The Washington Post in advance of its release.

One of the people familiar with the White House deliberations attributed the moving target in part to a review the White House is conducting of policy developments, progress and legal considerations relevant to the decision.

The people familiar with the deliberations, like others interviewed for this report, spoke on the condition of anonymity to describe private talks and emphasized that no final decisions have been made and that the timing of an announcement was up in the air. The White House has changed course abruptly before, including over the span of several hours on a single day this month, giving people inside and outside the building pause about drawing definitive conclusions about the plan.

During the daily press briefing on Tuesday, Psaki declined to say how likely it was that the president would set the new cap at 62,500. “If the cap is at that or close to that, it will continue to be challenging,” Psaki said.

She said one of the considerations at the White House is what message the nation is sending abroad. “We want to send a clear message, we are welcoming refugees,” she said. The 62,500 number was “always meant to be a down payment” on Biden’s larger pledge for the next fiscal year, Psaki said.

The United States has welcomed refugees — people seeking admission to escape persecution, oppression or warfare overseas — for decades. Presidents are empowered to set annual targets for how many people to try to admit.

The Post reported last week that after he announced he was lifting the cap in early February, Biden grew concerned about the government’s response to the surge of unaccompanied children at the U.S.-Mexico border, prompting a delay in issuing a new directive that frustrated and confused his allies.

On April 16, the White House announced that it would in the meantime keep in place a record-low cap of 15,000 set by the Trump administration last year. Biden overruled his top foreign policy and national security aides, including Secretary of State Antony Blinken, in deciding to keep the cap. The White House backtracked later that day after fierce blowback from allies.

Psaki said late that day that Biden was expected to set a final, increased cap by May 15 but gave little indication of what it would be, beyond suggesting that the number of refugees the president had previously aimed to admit was probably not feasible. “Given the decimated refugee admissions program we inherited, and burdens on the Office of Refugee Resettlement, his initial goal of 62,500 seems unlikely,” she said in a statement.

The unusual delay underlined the broader political concerns about immigration politics and policy shared by Biden and his top advisers. The president's own misgivings fueled the decision more than anything else, according to people familiar with the matter. Now, Biden’s own initial opposition to raising the cap injects uncertainty into the ultimate decision.

The latest machinations follow intense private and public pressure from refugee advocates, who have lashed out at the White House for backing away from its promise. In a private videoconference last week, the heads of resettlement agencies who work with the government vented their frustration with White House aides, according to two people with direct knowledge of the conversation.

Ernesto Apreza, a senior adviser for public engagement at the White House, acknowledged during the call that administration officials needed to do a better job of keeping the refugee resettlement groups informed. The White House outreach in recent months “falls very short” of what it should have been, Apreza said, according to a person with direct knowledge of his comments.

Resettlement agency heads vented frustration about the White House strategy during the conversation. Mark Hetfield, the president of HIAS, a Jewish refugee resettlement organization, said the “talking points” he kept hearing from Psaki and others suggested that Biden has “an unwavering commitment to the refugee program.” Hetfield argued that the commitment “wavered for over two months,” according to a second person with knowledge of the conversation.

The tone of the letter senators sent Tuesday is more measured than the reaction some of them had after the earlier announcement.

Biden, in a speech at the State Department on Feb. 4, signaled that he would be much more welcoming of refugees than Donald Trump was as president. He vowed to raise the annual cap to 125,000 for the next fiscal year, which begins in October. On Feb. 12, his administration identified that more immediate step in a report sent to Congress: increasing the cap to 62,500 for the current fiscal year.

But the White House went quiet on the matter for about two months and Biden did not sign the directive known as a presidential determination. In the past, signing the paperwork was seen as a formality.

As the White House offered little explanation for its actions, criticism from Democrats and refugee advocates grew. Then, on April 16, the White House abruptly announced that it was not immediately raising the cap from 15,000.

That same day, Biden changed the regional allocation of refugees, loosening the restrictions Trump had placed on people coming from some African and Muslim-majority countries. Refugee advocates have cheered those efforts.

The president’s increasing concerns during the spring about the Office of Refugee Resettlement’s response to the surge at the border drove the delay, the people familiar with the matter said. The office is part of the Department of Health and Human Services and is responsible for both unaccompanied minors at the border and foreigners seeking refugee status.

Some refugee advocates have not been satisfied by this explanation, arguing that there is enough separation between the two responsibilities to ensure one should not have a huge impact on the other.

Psaki recently said that Biden “remains committed to the aspirational goal” of 125,000 for the next fiscal year.