The Afghan government has called for a humanitarian ceasefire with the Taliban, as the first-ever peace talks between the two sides began in Qatar.
Abdullah Abdullah, who led the government's delegation, stressed that there was “no winner through war”.
The Taliban did not mention a truce, reiterating instead that Afghanistan should be under Islamic law.
The US encouraged both sides to reach an agreement, telling them: “The entire world wants you to succeed”.
Afghanistan has seen four decades of conflict, with tens of thousands of civilians killed.
The historic talks began on Saturday, one day after the 19th anniversary of the deadly 9/11 al-Qaeda attacks in New York, that led to the US beginning military operations in Afghanistan.
The conflict in Afghanistan has been the longest in US history.
Why are these talks so important?
These are the first direct talks between the Taliban and representatives of the Afghan government. The militants had until now refused to meet the government, calling them powerless and American “puppets”.
The conflict is still continuing in Afghanistan, and the government says 12,000 civilians have been killed since February.
At Saturday's opening ceremony, the head of Afghanistan's peace council, Abdullah Abdullah, called for an immediate ceasefire, telling Reuters “one of the top most issues on the minds of the people is reduction in violence in a significant way”.