David Cameron said the US talking to the Taliban was "the right thing to do" despite the difficulties.
A Taliban official in Qatar said no date has been set for peace talks with the Afghan government.
The Taliban are ready to hold peace talks with the Afghanistan government as well as the United States, a senior Afghan official told Reuters.
A representative of the Taliban announced the opening of a "political office" in Qatar live on television.
The Taliban will release a statement today saying that they oppose the use of Afghan soil to threaten other countries and support peace, US officials told Reuters.
The US has welcomed the statement and sees it as an "important first step towards reconciliation".
The United States see the Afghanistan peace talks with the Taliban as only the first step in what is likely to be a complex and "messy" process, officials told Reuters.
The US will insist that the Taliban and insurgent groups break ties with al-Qaeda, end violence and accept the Afghan constitution which includes protection for women and minorities.
The United States and the Taliban will engage in Afghanistan peace negotiations in Doha next week, senior US administration officials told Reuters.