US Special Representative for the Peace Process Zalmay Khalilzad called on all parties to reduce violence.
Zalmay Khalilzad met with Taliban leaders in Doha yesterday after meeting with Afghan government leaders in Kabul.
"I told the Taliban that violence on all sides must end," Zalmay Khalilzad said in a tweet on the social networking site Twitter.
"I had three consecutive meetings with Mullah Baradar and members of the Taliban's political affiliations," he said.
Intra-Afghan negotiations included in the US-Taliban agreement, withdrawal of troops, and a permanent ceasefire with a gradual reduction in violence were discussed.
Earlier, he met with Afghan President Ashraf Ghani and his former rival Abdullah Abdullah in Kabul.
Yesterday, Mullah Hebatullah Akhundzada, the supreme leader of the Afghan Taliban, announced a general amnesty for his opponents on condition that they renounce enmity.
That every male and female member of society will be given this right.
In a message issued before Eid al-Fitr, the Taliban leader specifically said that the "Islamic Emirate" had no monopoly policy.
And assured that every man and woman in Afghan society will be given their rights so that no one feels deprived or unfair.
The Taliban leader said, "We urge everyone to give up their opposition and take full advantage of the amnesty."
And do not stand in the way of the establishment of an Islamic government that is the wish of millions, martyrs, wounded, disabled, orphans, widows, and suffering Afghans.
In addition, on May 19, four countries in the region called on Afghan groups to agree to a ceasefire, start peace talks as soon as possible and take decisive action against terrorist groups on their soil.
The demand was made in a joint statement issued after a "virtual" meeting of delegates from Pakistan, Iran, Russia, and China on the current situation in Afghanistan and issues facing the peace process.
It should be noted that a peace agreement was signed between the United States and the Taliban on February 29 in Doha, the capital of Qatar, in which it was agreed that
The Afghan government will release 5,000 Taliban prisoners in exchange for the release of 1,000 government prisoners.
The prisoner exchange was due to be completed before March 10 and negotiations between the Taliban and the Afghan government were to begin, but the process was slow due to a number of issues.
However, the recent wave of violence in Afghanistan has further complicated the issue, with some of the attacks, including the May 12 attack on a maternity hospital attributed to ISIS.
After Afghan President Ashraf Ghani ordered the resumption of offensive operations against the Taliban, the Taliban said in response to the Afghan government's announcement that they were fully prepared to respond to attacks by Afghan forces.
The Taliban had said that from now on, the responsibility for further tensions would fall on the shoulders of the Kabul administration.
Earlier on May 18, the Taliban reiterated its demand for implementation of the Doha Accords, said Sohail Shaheen, a spokesman for the Taliban's political office in Doha.
That the solution to the Afghan problem lies in the implementation of the Doha Agreement, the release of prisoners should be completed and inter-Afghan talks should begin.
However, the Taliban attacked Kunduz the same night, the Afghan Ministry of Defense said, adding that the attack was foiled and the Taliban suffered heavy losses.