The minister, Amir Khan Muttaqi, also said Washington would offer Afghans coronavirus vaccines.
It was the first senior face-to-face meeting between the two sides since the hardline group took over the country in August following a US troop pullout.
The minister added that the Afghan delegation and US counterparts discussed “opening a new page” between the two countries, adversaries during the United States’ two-decade long occupation of Afghanistan.
Washington and other Western countries are grappling with difficult choices as a severe humanitarian crisis looms large over Afghanistan.
They are trying to formulate how to engage with the Taliban without granting it the legitimacy it seeks while ensuring humanitarian aid flows into the country.
The departure of US-led forces and many international donors robbed the country of grants that financed 75 per cent of public spending, according to the World Bank.
Speaking to Reuters earlier in Washington, a US official said that while there was an improvement for humanitarian actors to get access to some areas that they haven’t been to in a decade, problems still persisted, adding that the US delegation at the Doha talks would press the Taliban to improve.
Mutaki also said that the Afghan delegation focus at the meeting was humanitarian aid and implementing Doha agreement.
He said the discussions would continue on Saturday and would resume on Sunday.
Mutaki added the Afghan delegation will meet European Union representatives to discuss latest developments, but he didn’t mention when the meeting will be held.