President Trump’s declaration that the United States and Iran had reached a preliminary agreement to halt hostilities drew cautious optimism and frustration from lawmakers on Capitol Hill, where even some Republicans were reluctant to praise a deal whose terms the administration has yet to disclose.

“We do not have an agreement just yet, so we will see when there is text out there,” Senator John Thune, Republican of South Dakota and the majority leader, told reporters at the Capitol. “I’m guessing there will be a high level of interest among our members.”

As they returned to Washington on Monday, senators in both parties said they welcomed any path away from war, but questioned why Congress had yet to receive details of a deal that could reshape U.S. involvement in the Middle East.

“If it is a secret deal, then how can I take it seriously?” Senator Thom Tillis, Republican of North Carolina, said Monday afternoon.

Mr. Thune said he expected the administration to brief lawmakers on the pact, and Democrats were demanding that top officials do so.

“It’s been nearly 24 hours since Trump announced there was a potential deal with Iran, and we still don’t know the details,” Senator Chuck Schumer of New York, the minority leader, said in a speech from the Senate floor. “Trump must brief Congress and the public on the details of his understanding with Iran immediately and end this war once and for all.”

Both Mr. Thune and Mr. Schumer are members of the so-called Gang of Eight in Congress that is supposed to be briefed on highly classified intelligence matters.

Senator Jeanne Shaheen of New Hampshire, the top Democrat on the Foreign Relations Committee, said in a statement that Congress must be “immediately briefed on the terms of this agreement,” adding that any nuclear deal reached would have to be approved by the Senate “by law.”

From the outset, the administration has withheld information from Congress about the war in Iran, and Republican leaders for months refrained from conducting any oversight. But in recent weeks, some of them have joined Democrats in urging the administration to be more forthcoming.

On Monday, some Republicans maintained their deferential posture despite receiving no details about the deal.

“President Trump deserves our trust and support as he works to bring peace to the Middle East,” Senator Bernie Moreno, Republican of Ohio, said in a statement.

But G.O.P. hawks injected a pointed note of skepticism.

“I look forward to reviewing the actual document rather than relying on Iranian propaganda reports,” Senator Lindsey Graham, Republican of South Carolina, wrote on social media, where he avoided directly attributing the agreement to the president and instead said it had been “envisioned by the Vice President and the Trump Administration.

“The sooner it is released,” Mr. Graham wrote, “the better.”

Even some Republicans who voiced optimism about a possible deal maintained that any final agreement on Iran’s nuclear program would have to go through Congress.

Senator Mike Rounds, Republican of South Dakota, noted that the nuclear pact the Obama administration reached with Iran in 2015 had not been ratified by Congress and was therefore nonbinding. If the Trump administration wanted a forthcoming nuclear agreement to “be something other than a political agreement,” he said, it needed to be ratified by the Senate.