The Taliban has said peace talks in Moscow with other factions in Afghanistan have made "spectacular progress" on some issues. Russia has sought to play power broker in Afghanistan and is attempting to mediate between warring factions as it jockeys with Washington for influence in a country where a US-led coalition has been fighting for more than 17 years.
The latest negotiations, which wrapped up on Thursday, follow a previous round in February.
"We discussed all important issues and we made some progress, spectacular progress, on some issues and it will continue at our next meetings," said Suhail Shaheen, spokesman for the Taliban's political office in Doha.
We are talking here to bring about peace in Afghanistan and to put an end to the current occupation and to form a future government in Afghanistan, which is participated in by all Afghans.
Ata Mohammad Noor, a powerful ex-governor of the northern Balkh province who now heads the Jamiat-e Islami party, also noted some progress, but added that he had expected more.
"Yesterday we negotiated for hours and we did come to some agreement, but our expectations were higher," Mr Noor said. "We had at least nine hours of negotiations. Our main message was on the ceasefire, a ceasefire could be the beginning of peace."
Greeting representatives of various Afghan factions earlier this week at a ceremony marking the centenary of diplomatic relations, Russian foreign minister Sergey Lavrov emphasised that Russia stands for the full withdrawal of foreign troops from Afghanistan and called for comprehensive peace talks.
Zamir Kabulov, President Vladimir Putin's envoy for Afghanistan, said he met with the Taliban to discuss "ways to help speed up the process of national reconciliation in Afghanistan".