If the American side accepts the offer, it could amount to the most significant development in the yearlong negotiations since talks resumed after President Trump had scuttled the peace process on the eve of a deal in September.
Though the pledge to reduce violence falls short of the overarching long-term cease-fire sought by the Afghan government, Western diplomats had said getting the Taliban to agree to more than a modest reduction in attacks would be difficult before the withdrawal of foreign forces gets underway.
Details of the offer, confirmed by Western and Taliban officials familiar with the negotiations, were unclear, though the Taliban have said in the past that a reduction in violence would mean scaling back attacks on major cities and highways.
Also unclear was the duration of any reduction — though one Taliban official suggested it was between seven and 10 days — and whether the American side had agreed to the Taliban proposal, which was made on Wednesday.
But the offer appears to have put the talks in Doha into a new phase. Soon after midnight, the Taliban negotiating team’s spokesman, Suhail Shaheen, said the two negotiating teams had talked about details of “the signing of the agreement and the ceremony for it.”
“The talks will continue for the coming days,” Mr. Shaheen said on Twitter.
In another sign that a deal could be closer, the top commander of United States and NATO forces in Afghanistan, Gen. Austin S. Miller, joined the American negotiating team in Doha, officials said.
The issue of whether to agree to a cease-fire before the departure of the roughly 13,000 American forces and thousands more NATO troops has been an existential one for the Taliban, who see violence as their most important leverage. The insurgents spent more than a month deliberating Washington’s demand.
Members of the Taliban negotiating team repeatedly traveled from Doha, Qatar, where the talks are taking place, to consult with the group’s leaders and commanders in Pakistan, where they enjoy havens. In the end, they came back to the Americans with a proposal of reducing violence for a brief period.
Some officials suggested the arrangement could essentially amount to a cease-fire — in which no attacks are carried out — without explicitly using the term, which some Taliban leaders believe would divide their ranks.
In the past, the Taliban have refused to talk with the Afghan government, calling it an American puppet. But in September, before Mr. Trump scuttled a nearly signed peace deal, a round of negotiations that was to include some members of President Ashraf Ghani’s administration had been planned in Oslo for soon after the signing of a deal between the Taliban and the United States.
The Afghan government still seemed to be pushing for an extensive cease-fire. Hamdullah Mohib, the national security adviser, said at a conference in New Delhi on Wednesday that Afghan leaders saw a cease-fire as a sign of the Taliban’s seriousness for genuine peace, and that the group — which the government has long seen as a proxy of the Pakistani military — can deliver on what they sign.
“Peace for our people means the end of violence,” Mr. Mohib said. “This is why we insist that a cease-fire is necessary to create a conducive environment for talks.”
A cease-fire, he added, “will prove to the Afghan people and government that our enemies are not only serious about peace, but that it is within their control to maintain their part of a future deal.”
Mr. Trump’s scuttling of the talks threw into confusion American policy on Afghanistan, and raised fears that Mr. Trump, long public about his weariness with the war, might pull troops from the country even without a deal. But it also provided a window of reflection over a peace process that many saw as too rushed.
Afghan leaders, which had worried that their American allies were selling them out, saw an opportunity for course correction and urged a complete reset that emphasized a cease-fire as a condition for any resumption of talks.
The Taliban used the break to bridge divides in their own ranks, most notably the suspicions of many in the military over any deal. Mullah Abdul Ghani Baradar, the Taliban deputy leading the talks, traveled to Pakistan and held several large meetings, some with as many as 300 senior and midlevel commanders and officials, to bring them onboard with what he said was the best deal he could negotiate.
About a month into the lull, American diplomats, led by the chief negotiator Zalmay Khalilzad, began quietly looking at trust-building measures that could put the negotiations back on track. That included releasing several senior Taliban leaders from prison, a move officials hope Taliban negotiators can use to prod their own military to agree to reduce violence.
During his first visit to Afghanistan in November, Mr. Trump announced the resumption of negotiations. He said the Taliban were interested in a cease-fire. His remarks, which seemed to echo the Afghan government’s desire, appeared to catch both the militants and his own officials off guard. But both sides returned to the table in hope of finding ways to significantly reduce the bloodshed so the deal could move forward.
Mujib Mashal reported from Kabul, and Taimoor Shah from Kandahar, Afghanistan. Fahim Abed contributed reporting from Kabul and Thomas Gibbons-Neff from Washington.