In a statement posted last night, the Taliban said it "calls on American officials to talk directly to the Political Office of Islamic Emirate regarding a peaceful solution to the Afghan quandary", using its official name.
There has been no response to the offer from US officials, who have historically insisted any talks must include the Afghan government in Kabul.
The call for talks comes a day before the second round of a regional peace conference in Kabul, where representatives from 25 countries will discuss counter-terrorism and conflict resolution strategies.
The Taliban published an open letter to the American people and the US Congress earlier February, suggesting the insurgents may be ready for talks.
The apparent openness to negotiations is unusual for the militant group, which has repeatedly stated that it will not enter talks until foreign troops leave the country.
Unveiling his new Afghan strategy last August, Trump said the US presence in Afghanistan would remain open-ended, as Washington stepped up strikes on militant strongholds.
In January, Trump ruled out holding talks with the Taliban, after a spate of assaults in Kabul.
The attacks included an assault on the capital's luxury Intercontinental Hotel, an ambulance bomb in a crowded street and a raid on a military compound, that killed more than 130 people.
As violence intensifies nationwide, the Afghan capital will host the Kabul Process tomorrow, focusing on rebooting peace talks and uniting regional countries in the fight against terrorism.
"At the Kabul conference, we will present a comprehensive peace plan for Taliban and Pakistan," Afghan President Ashraf Ghani said today.
The conference follows an earlier meeting held in June last year.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)