U.S. and Taliban officials will reconvene in Doha, Qatar on Tuesday to continue peace talks described as the "most productive session" by a top U.S. negotiator leading the discussions with the hardline Islamists group to end the Afghan war.

The warring sides started a seventh round of peace talks last week, aiming to hammer out a schedule for the withdrawal of foreign troops in exchange for Taliban guarantees that international militant groups will not use Afghanistan as a base to launch attacks.

In a tweet on Saturday, U.S envoy Zalmay Khalilzad, who has been holding peace talks with the Taliban to end the 18-year war in Afghanistan since last year, said the latest round of discussions were the "most productive session" to date.

He said substantive progress had been made on all four parts of a peace deal: counter-terrorism assurances, troop withdrawal, participation in intra-Afghan dialogue and negotiations, and a permanent and comprehensive ceasefire.

About 20,000 foreign troops, most of them American, are in Afghanistan as part of a U.S.-led NATO mission to train, assist and advise Afghan forces. Some U.S. forces carry out counter-terrorism operations.

On a trip to Kabul last month, U.S. Secretary of State Mike Pompeo said the United States was close to finishing a draft agreement with the militants on counter-terrorism assurances, adding he hoped a peace pact could be reached by September 1.

Khalilzad, an Afghan-born American diplomat, wants to secure a political settlement with the Taliban, which now controls more Afghan territory than at any time since being toppled in 2001 by U.S.-led forces.

"There is still important work left to be done before we have an agreement," he said, adding the ongoing peace talks will resume on July 9 after the intra-Afghan dialogue.

Clarity on a final agreement on the timetable of foreign force withdrawal has been elusive so far, but in a sign of progress the Taliban agreed on the sidelines of the peace talks to hold separate discussions with a group of Afghan delegates.

Both sides decided on Saturday to put the peace talks on hold for two days, to allow for a meeting between rival Afghan groups to be held in Qatar, Taliban and U.S. officials said.

U.S. officials are demanding a ceasefire agreement and a commitment on direct talks between the Taliban and the Afghan government before a peace deal is finalized.

Sohail Shaheen, a spokesman for the Taliban’s political office in Doha, said the ‪U.S.-Taliban dialogue would resume after the two-day intra-Afghan conference.

A previously planned meeting between Afghan representatives in April collapsed before it started amid disagreement over the size of the proposed 250-strong Afghan delegation as well as over its status as a representative body.

This time, about 40 high-profile Afghan figures and activists will fly to Doha but will not have any official status — a condition made necessary by the Taliban’s refusal to deal directly with the Western-backed government in Kabul.

The Taliban have stressed that those attending the talks planned for Sunday and Monday will only do so in a "personal capacity."

A senior Taliban official, speaking on condition of anonymity, said ensuring the protection of the rights of women and minorities would be discussed in the Doha talks, which have been facilitated by German and Qatari officials.

Despite intensified diplomatic efforts to end the 18-year long war in Afghanistan, deadly violence has surged across the country.

Last week, the Taliban claimed a truck bomb attack in Kabul that killed six people and wounded 105 civilians, many of them children.