The renewed fighting coincides with a two-day round of peace talks now underway in Moscow between Taliban representatives and several Afghan officials, who are not affiliated with the Kabul government.
The two-day meeting in the Russian capital between the Taliban and Afghan figures, which starts Tuesday, is seen as another step in a process aimed at resolving Afghanistan's 17-year war, one that has accelerated since the appointment last September of USA peace envoy Zalmay Khalilzad.
Among Afghans invited to the gathering are former President Hamid Karzai; Haneef Atmar, a former national security adviser to Ghani and his key rival in July's presidential election; and a number of factional leaders such as Ismail Khan, Mohammed Mohaqeq and Atta Mohammad Noor.
The Taliban's deputy chief negotiator, Salam Hanafi, also said the group will negotiate directly with Kabul once the U.S. announces a full withdrawal.
The Taliban demanded a new constitution for Afghanistan and promised an "inclusive Islamic system" to govern the war-torn country at a rare gathering with senior Afghan politicians in Russian Federation on Tuesday that excluded the Kabul government.
"Peace talks with the Taliban continue, but [the Defense Department] has not received a directive to change the force structure in Afghanistan", said Manning.
Hanafi said Washington and the Taliban had agreed at talks that all foreign troops would eventually leave, and that Afghanistan would never be used as a base for attacks on the United States. They admitted Afghan forces suffered casualties but would not reveal any figures. The Taliban closed girls' schools and banned women from working under their regime, but have indicated they could loosen some guidelines in line with Sharia law.
But Pentagon spokesman Army Colonel Rob Manning said the United States military had received no orders to begin withdrawing.
Ghani's call to Pompeo seemed an attempt to re-assert his government's role in negotiations he has sharply criticized at times as one-sided.
President Ashraf Ghani has insisted on leadership and ownership of the peace process by Afghans who he said wanted "a dignified and stable peace" in their country.
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Lead Taliban negotiator Sher Mohammad Abbas Stanikzai told reporters that the movement did not want to rule alone but as part of "an intra Afghan Islamic system of governance.in consultation with all Afghans".
USA and Taliban delegations met in Qatar in January and are due to meet again in February.
"The Moscow meeting is nothing more than a fantasy". Peace needs the consensus of all Afghans.
At least 36 members of the Afghan security forces and 22 Taliban fighters have been killed in fresh clashes in the country's north, officials and local media confirmed Tuesday.
He said that Moscow talks indicate that Afghans have the determination and the will to open a new chapter to solve the issues and that Afghans and Taliban should come together to resolve their differences.
Ghani's government has so far been shut out of the evolving peace talks between Taliban negotiators and U.S. envoys to end more than 17 years of war, with the hard-line Islamist movement branding his government a U.S. puppet.
Participants gather before a conference of Afghan opposition and Taliban representatives, in Moscow, Russia, Feb. 5, 2019.
Now the exact timetable for the pullout must be decided, but the Taliban wants to see this happen in months, he said.
The meeting in Moscow is separate from the US-Taliban peace talks. The present Afghan military forces and the Taliban need to cooperate in this regard, which will not be easy to accomplish. "But Afghans prefer a democracy which will be compatible to our values", said Qanooni.