An agreement would allow President Donald Trump to achieve his aim of ending Washington's longest-running war, launched after the September 11, 2001 attacks on the US.
The latest round of talks between the Taliban and the United States on a deal to withdraw thousands of US troops from Afghanistan has ended. Now both sides will consult with their leadership on the next steps, a Taliban spokesman said Monday.
The eighth round of talks in the Gulf Arab nation of Qatar concluded after midnight and was "long and useful," Zabihullah Mujahid said in a statement.
He made no statements on the outcome of the talks.
Last week, another Taliban spokesman had said a deal was expected to follow this round as both sides seek an end to the nearly 18-year war, America's longest conflict.
An agreement — if reached — is expected to include Taliban guarantees that Afghanistan would not be a base for other extremist groups in the future.
However, both Daesh's affiliate and al Qaeda remain active in the country.
The Taliban stage near-daily attacks across Afghanistan, mainly targeting Afghan forces and government officials but also killing many civilians.
The deal also could include a ceasefire and stipulate that the Taliban would negotiate with Afghan representatives, though the insurgent group has so far refused to negotiate with Kabul representatives, dismissing the Afghan government as a US puppet.
There was no immediate comment on Monday from US envoy Zalmay Khalilzad, who on Sunday tweeted that "I hope this is the last Eid where #Afghanistan is at war."
Sunday was the first day of the Muslim holiday of Eid al Adha, which unfolded without any major violence reported in Afghanistan.
Khalilzad later added that "Many scholars believe that the deeper meaning of Eid al Adha is to sacrifice one's ego. Leaders on all sides of the war in Afghanistan must take this to heart as we strive for peace."
Some in Afghanistan saw it as a response to President Ashraf Ghani, who on Sunday declared that "Our future cannot be decided outside, whether in the capital cities of our friends, nemeses or neighbours. The fate of Afghanistan will be decided here in this homeland. ... We don't want anyone to intervene in our affairs."
While Ghani insists that the upcoming September 28 presidential election is crucial for giving Afghanistan's leader a powerful mandate to decide the country's future after years of war, Khalilzad is seeking a peace deal by September 1, weeks before the vote.
The Taliban control roughly half of Afghanistan and are at their strongest since the US-led invasion toppled their five-year government in 2001 after the group had harboured Osama bin Laden saying it would hold a trial of the al Qaeda leader if Washington provided evidence.
More than 2,400 US service members have died in Afghanistan since then.
The US and NATO formally concluded their combat mission in Afghanistan in 2014.
The some 20,000 American and allied troops that remain are carrying out airstrikes on the Taliban and Daesh, and are working to train and build the Afghan military.