Senate Republicans cast doubt on the viability of a potential peace deal between the United States and Iran over the weekend as President Trump doubled down in support of his administration’s negotiations to end the nearly three-month-old war.

U.S. and Iranian officials have described an emerging framework that would reopen the Strait of Hormuz and in which, U.S. officials say, Iran would commit to disposing of its highly enriched uranium. Iranian officials have also said that nuclear matters would be negotiated within 30 to 60 days.

“It doesn’t make too much sense to me,” Senator Thom Tillis, Republican of North Carolina, said Sunday on CNN’s “State of the Union.” Mr. Tillis called the Iranians’ commitment to reopening the Strait of Hormuz “questionable” without a finalized peace deal, adding that “there are a lot of things that need to be explained.”

On Saturday, Senator Roger Wicker, the chairman of the Senate Armed Services Committee, wrote on social media that a “60-day ceasefire — with the belief that Iran will ever engage in good faith — would be a disaster.”

Mr. Trump shot back on social media on Sunday afternoon, calling any deal he would negotiate “good and proper” and saying that such criticism was coming from “losers, who are critical about something they know nothing about.” He had announced on Saturday that the United States and Iran “largely negotiated” an agreement to end the war.

But even some of the president’s closest allies have expressed misgivings. Senator Lindsey Graham, Republican of South Carolina, wrote on social media on Saturday that striking a peace deal now would fuel the perception that the United States was recognizing Iran as a dominant force “requiring a diplomatic solution,” calling such an outcome “a nightmare for Israel.”

“It makes one wonder why the war started to begin with,” he added.

Senator Ted Cruz, Republican of Texas, said he was “deeply concerned” about the prospective deal, calling any outcome in which Iran retained control of the Strait of Hormuz and the ability to enrich uranium “a disastrous mistake.”

Some Republicans, however, including Speaker Mike Johnson, still voiced support for a deal and cautioned against making a quick judgment before its official terms were released.

Mr. Johnson said Sunday on “Fox & Friends Weekend” that he was “confident” that the deal would “take care of the nuclear dust” (Mr. Trump’s term for Iran’s stockpile of enriched uranium) and praised the president for his “resolute” will to curb Iran’s nuclear ambitions.

Senator Rand Paul, Republican of Kentucky and a frequent critic of Mr. Trump’s policies, encouraged patience from other critics of the administration, saying on social media on Sunday that they “should give President Trump the space to find an American first solution.”

Senate Democrats, for their part, also joined in with critiques on Sunday. Senator Cory Booker of New Jersey said on CNN that the president was “being played as a fool,” while Senator Chris Van Hollen of Maryland called the emerging framework “a return to the prewar status quo.”

Annie Karni and Taylor Robinson contributed reporting.