"They confirmed they were ready for such talks with the Americans," Kabulov, who also serves as the head of the Russian Foreign Ministry's Second Asian Department, said.
When asked if there already was an agreement on a new meeting, he said, "They don't know, and neither do I."
According to the diplomat, lifting of UN Security Council sanctions on the movement was not discussed at the meeting.
"No, we did not discuss this issue," Kabulov said.
The statement comes after last week Trump called off secret Camp David meetings with the Taliban and Afghan President Ashraf Ghani. Reacting to Trump's decision, the Taliban vowed to continue fighting against American forces in Afghanistan, while the US president said the US forces had "hit our enemy harder than they have ever been hit before and that will continue."
Trump's move was prompted by several terrorist attacks conducted in early September and claimed by the Taliban. On 2 September, a huge explosion hit Kabul's PD9 district, where foreign troops and agencies are located, just hours after US Special Representative for Afghanistan Reconciliation Zalmay Khalilzad shared with the nation's leadership the details of a peace deal drafted during the ninth round of talks in the Qatari capital of Doha.
Three days later, three explosions rocked Kabul, killing dozens of people, including a US soldier.
* The Taliban - a terrorist group banned in Russia and many other countries.