1217 GMT January 18, 2021
The meetings, which began in September, had been bogged down by disputes on the agenda, the basic framework of discussions and religious interpretations, AFP reported.
Nader Nadery, a member of the government's negotiating team, tweeted that "procedures for the intra-Afghan negotiations... had been finalized and discussions on the agenda" would follow.
Mohammad Naeem, a spokesman for the Taliban, also tweeted that procedures for the talks had been "finalized and from now on, the negotiations will begin on the agenda".
The warring sides have been engaging directly for the first time following a landmark troop withdrawal deal signed in February by the insurgents and Washington.
The US agreed to withdraw all foreign forces in exchange for security guarantees and a Taliban pledge to hold talks with Kabul.
Abdullah Abdullah, chairman of Afghanistan's High Council for National Reconciliation, in a tweet called the development an "initial major step".
Pakistan’s Foreign Ministry in a statement welcomed announcement regarding the agreement reached on rules and procedures for the intra-Afghan negotiations by the Afghan parties.
“This is another significant step forward,” the statement said.
“The agreement reflects a common resolve of the parties to secure a negotiated settlement. It is an important development contributing towards a successful outcome of intra-Afghan negotiations, which we all hope for,” the statement added.
Washington's special envoy on the conflict Zalmay Khalilzad also welcomed the breakthrough, tweeting that it was a "significant milestone".
He said the two sides had agreed on a "three-page agreement codifying rules and procedures for their negotiations on a political roadmap and a comprehensive ceasefire".
"This agreement demonstrates that the negotiating parties can agree on tough issues," he added.
While both sides' negotiators had been ready to proceed with the talks, sources said that President Ashraf Ghani had objected to wording in the proposed ground rules that referred to his administration and the Taliban on an equal basis as "parties to the war".
It is unclear whether the wording was altered.
There has been a surge of violence in Afghanistan in recent weeks.
The Taliban militants have launched near daily attacks against Afghan forces, primarily in rural areas, since signing the deal with Washington in February that paved the way for the withdrawal of foreign troops by May 2021.