"Any negotiations over the political future of Afghanistan will be between the Taliban and Afghan government", State Department spokeswoman Stephanie Newman told CNN.
The Pentagon has 15,000 troops there trying to win a 17-year war started by President George Bush in a bid to destroy al-Qaeda's strongholds. He said the meeting was held in Qatar, where the Taleban maintained a political office since 2013. The department has confirmed that Wells was in Doha, but did not say whether she held a face-to-face meeting with Taliban representatives.
Speaking on the condition of anonymity, the Taliban official further added that the talks were held in a "very cordial atmosphere and both sides had useful exchanges", he added.
It was the first ceasefire since the US invaded Afghanistan to rout the Taliban after the 2001 9/11 attacks.
When he announced his new war strategy previous year, Trump declared that Taliban and Islamic State insurgents in Afghanistan "need to know they have nowhere to hide, that no place is beyond the reach of American might and American arms".
Late last week, a delegation from the US State Department was in Qatar to meet with Taliban officials.
A former Taliban minister also confirmed that a meeting between USA officials and the Taliban took place earlier this week in Doha.
The Afghan government is now considering another ceasefire in August.
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The Taleban argued that the Afghan government can not act independent of Washington.
During a news conference last month in Brussels, Gen. John W. Nicholson Jr., the commander of the American-led coalition in Afghanistan, said remote outposts were being overrun by the Taliban, which was seizing local forces' vehicles and equipment.
A US-led invasion drove the hardline Taliban from power in 2001, as part of a crackdown against Islamist militants in the wake of the 9/11 attacks.
The current leadership, most of whom are Mullah Omar's contemporaries, still believe their future in Afghanistan can be guaranteed only if the United States' concerns are addressed.
Back in February, Afghan President Ashraf Ghani called on the Taliban to join peace talks "without preconditions".
British ambassador to Afghanistan Sir Nicholas Kay said on Sunday the British government supports all efforts to get the Taliban to the negotiation tables.
The Taliban have repeatedly declared that they would not enter talks until USA -led foreign troops left the country.
The U.S. still has around 14,000 troops in Afghanistan after President Trump chose to increase the U.S. military's presence there by several thousand previous year.