He said the conditions for peace have improved and that it is clear all sides want to end the war.
Zalmay Khalilzad said that "there is no final agreement until everything is agreed".
The US had asked Pakistan to assist in its efforts to find a negotiated peace with the Taliban to end the longest war in American history.
Khalilzad said the Taliban and "other Afghans, including the government", will begin intra-Afghan negotiations on a political settlement and comprehensive ceasefire after the draft agreements concerning withdrawal timeline and effective counterterrorism measures are finalized.
The last round of talks in January led the United States and the Taliban to agree on a "draft framework" on a troop withdrawal and counterterrorism measures. "We're now "agreed in draft" on the first two", he said in a tweet.
A spokesman for Afghan President Ashraf Ghani tweeted that he hoped to see a long-term ceasefire agreement and the start of direct talks between the government and Taliban soon. "Despite ups and downs, we kept things on track and made real strides", Khalilzad said, adding that another round is possible later this month after 16 days of negotiations in Qatar's capital, Doha.
The Taliban have held multiple rounds of peace talks with the American team led by Khalilzad but have so far refused to talk to the Afghan government.
Later on the Taliban said in a statement that the United States and Taliban had deep discussions on two issues agreed in January.More news: Trump blasts 'fake news' over Melania body double theory
More news: Korea election sees 99.99pc turnout: KCNA
More news: Kim Kardashian Covers 5 Years of Rent for Man Released From Jail
The Afghan government, which was not involved in the Doha negotiations, said it was pleased with the progress made.
It is unclear as yet when the next round of talks will take place.
The insurgent group's spokesman Mujahid, while talking to Afghan media over the weekend, again ruled out talks with the Afghan government, rejecting those associated with it as "American puppets" and insisting if his group engages in such a process it would be tantamount to recognizing America's "18-year-old occupation" of Afghanistan. In another province, officials said an air strike killed both Taliban fighters and civilians.
About 14,000 USA troops are based in Afghanistan as part of a US-led North Atlantic Treaty Organisation mission to train, assist and advise Afghan forces.
On March 1, at least 23 Afghan security forces were killed in a Taliban attack on a joint US-Afghan base in southwestern Afghanistan.
The talks in Doha focused on the withdrawal of USA troops and assurances that insurgents would not use Afghanistan's territory to stage future terrorist attacks - one of the initial aims of American policy in the wake of the 9/11 attacks back in 2001.
A US -led worldwide force has fought since then against a Taliban insurgency.
"That sequence is a large concession to Taliban that may keep process moving but at cost of transferring leverage from U.S.to Taliban", tweeted Laurel Miller, former USA acting special representative for Afghanistan and Pakistan.