A statement issued outlined the agreements reached by at least 40 delegates to a "non-official meeting" bringing together Taliban representatives, Afghan government figures and UN representatives at a two-day meeting held in Qatar.
The dialogue was a step toward a peace process that has proved elusive during a war that has killed tens of thousands of Afghans since the Taliban were driven from power by a 2001 U.S.-led military operation.
In a further blow for peace hopes, Taliban fighters killed at least 18 police early on Monday in attacks in the northeastern province of Badakhshan, a local official said.
Insurgents have also pressed an assault on Kunduz city, a provincial capital in the north.
In Qatar the delegates agreed that the Taliban should re-open a political office in Doha that caused a furore in 2013 when it was briefly inaugurated as part of a previous, failed attempt to start negotiations.
At the televised inauguration ceremony, the Taliban representatives raised the flag of their former regime, enraging then-president Hamid Karzai and dooming hoped-for talks.
Afghanistan's new leader, Ashraf Ghani, has made negotiations a priority since taking office last year.
The delegates also called for the removal of key Taliban leaders' names from a U.N. terrorism blacklist so they could travel to negotiations, according to the statement by the Pugwash Council, a global organisation that promotes conflict resolution. It co-hosted the talks with Qatar's government.
Pugwash said more than 40 representatives including several Afghan women had attended the Qatar meeting.
However, there was no progress on the main obstacle to a ceasefire - the continued presence of around 10,000 U.S. military trainers and counter-terrorism forces.
PLEDGES
The talks ended on Sunday with pledges to hold a similar dialogue in the future. The Afghan government has made no statement on them, though members of the country's High Peace Council attended.
One Taliban participant told Reuters an eight-member Taliban delegation had held direct talks with Afghan officials.
"The Afghan delegation and Qayyum Kochai, uncle of (Afghan) President Ashraf Ghani, demanded we stop our fighting and announce a ceasefire," he said.
The Taliban said they would not stop fighting until all foreign forces had left Afghanistan, he said.
The government delegation argued that most foreigners had already left and only trainers remained, who would also leave if the Taliban stopped fighting, he said.
