On an April withdrawal, he said: "It's our desire".
But Pentagon spokesman Army Colonel Rob Manning said the U.S. military had received no orders to begin withdrawing.
"The Russian ambassador to Afghanistan has knocked on the doors of all those invited to the meeting many times, urging for their participation", said Sebghatullah Ahmadi, spokesperson for Afghanistan's foreign ministry.
The US invaded Afghanistan in 2001 as a reaction to the 9/11 terror attacks, with the mission lasting until December 28, 2014.
The Doha and Moscow discussions, though entirely separate, both excluded the government in Kabul, where President Ashraf Ghani is seen as increasingly sidelined from key negotiations for peace in his country.
Pompeo also emphasized the importance of an intra-Afghan dialogue and the role of a cease-fire in ending the violence and making it possible for the Afghan government, other Afghan leaders and the Taliban to negotiate a political settlement, Palladino said.
The meeting comes on the heels of marathon talks between the Taliban and the United States in Doha that have been described as a breakthrough and the possible beginning of a negotiated peace that can bring stability to war-scarred Afghanistan.
The nine-point statement issued on behalf of all parties also agreed on the complete withdrawal of foreign troops from Afghanistan. After years of being on the fringes since the invasion of the Americans and their allies ousted them from power, the Taliban are now gaining acceptance as legitimate stakeholders in the Afghan political process.
Ghani's administration shunned the February 5-6 Russian-hosted initiative, which came after the USA announced it was close to reaching a framework agreement with the Taliban on ending the 18-year Afghan war, including on the withdrawal of foreign troops. They admitted Afghan forces suffered casualties but would not reveal any figures.
However, Trump's sudden announcement in December that he would withdraw US forces from Syria alarmed allies and many current and former USA officials, who worry that Islamic State militants remain a threat.
Still, Fawzia Koofi, a lawmaker and women's rights activist, said her participation in the talks was a good first step, even though she was one of only two women among the more than 20 Afghan figures who travelled from Kabul to Russian Federation.
In addition to departure of all foreign troops, the Taliban are demanding the end of USA bombing of civilians, a constitution that would respect the interests of all the people of Afghanistan, and guarantees for human rights and the rights of women.
Stanikzai further demanded the removal of Western sanctions and travel bans on Taliban members, prisoner releases, an end to "propaganda" against the Taliban and clearance to open an official office.
Safi Amiri, Deputy Provincial Council Chief of Kunduz province, told Efe news that Taliban fighters attacked check-posts on the outskirts of Kunduz city shortly after midnight.
"There is no need to reinterpret Afghan women's lives", the statement said. "Dissemination of western and non-Afghan and non-Islamic drama serials, paving way for immoral crimes, and encouraging women for violating Afghan customs are other instances that have been imposed on Afghan society under the name of women rights".
President Donald Trump delivered the State of the Union address, with Vice President Mike Pence and Speaker of the House Nancy Pelosi, at the Capitol in Washington, DC on February 5, 2019.
Fawzia Koofi, a member of the Afghan parliament and one of the two women to participate, said she received a cool reception from the Taliban when she pressed them on women's rights during closed-door meetings in Moscow.
The months-long push by the U.S. to engage the Taliban has ostensibly been aimed at convincing them to negotiate with Kabul.