Two senior Republican senators warned the Trump administration on Saturday to prepare for the possible expiration of a key tool for U.S. government surveillance, urging top officials to take steps to bridge any gaps in intelligence gathering.

In a letter to Secretary of State Marco Rubio, who is also the national security adviser, Senator Tom Cotton of Arkansas, the chair of the Intelligence Committee, and Senator Charles E. Grassley of Iowa, who leads the Judiciary Committee, said they believed that Section 702 of the Foreign Intelligence Surveillance Act may not be renewed before it expires on June 12, despite weeks of bipartisan negotiations aimed at preserving the program.

Those negotiations fell apart on Friday after Democrats refused to back a renewal because of concerns over President Trump’s recent appointment of Bill Pulte, a close ally and the federal housing director, to oversee the nation’s intelligence agencies. The defeat left uncertain the future of Section 702, which allows intelligence agencies to collect communications of foreign targets overseas — including when they are communicating with Americans.

In their letter, the senators urged the administration to identify intelligence targets that could be affected by a lapse, to explore alternative legal authorities to continue collecting intelligence and, if necessary, to draft an executive order to address the gap left by the expiration of the law. The letter was first reported by Punchbowl News.

What had appeared to be a relatively routine reauthorization effort has devolved into one of the most politically fraught national security debates of Mr. Trump’s second term.

Just weeks ago, lawmakers approved a short-term extension to buy negotiators time to work through proposed changes to the surveillance authority, which allows the government to collect the communications of foreigners overseas without a warrant.

Earlier this week, both Republicans and Democrats suggested that a bipartisan compromise had emerged, and that a longer-term extension was on track to pass.

Instead, a procedural vote to begin consideration of a three-year reauthorization failed Friday, with nearly every Democrat joining a bloc of Republicans in opposition.

The collapse has been fueled not only by longstanding concerns about government surveillance, but by Mr. Trump’s decision to install Mr. Pulte as the acting director of national intelligence, a move that bypasses Senate confirmation.

Lawmakers in both parties initially expressed alarm over Mr. Pulte’s lack of intelligence experience, and Democrats were intensely concerned with his reputation as an aggressive Trump loyalist who has sought to target some of the president’s perceived enemies.

Those concerns intensified after Mr. Trump told The Wall Street Journal that he hoped Mr. Pulte would conduct mass layoffs across the intelligence community. “I’d like to see it smaller,” Mr. Trump said. “I think there are a lot of people in there that shouldn’t be there.”

The episode has also exposed divisions in Mr. Trump’s own coalition.

The president has long been skeptical of Foreign Intelligence Surveillance Act authorities, and has argued that surveillance powers were used against him. But senior administration officials, including Stephen Miller, a top White House adviser, have mounted an aggressive campaign demanding that Congress renew the program.

That effort has triggered fierce pushback from some conservative lawmakers, including Representative Thomas Massie of Kentucky and Senator Mike Lee of Utah, who have framed the moment as an opportunity to force sweeping reforms.

“Senators are being told they MUST reauthorize FISA 702 without requiring a warrant for U.S. citizen queries,” Mr. Lee wrote in a social media post on Friday. “This is nonsense.”