It is the first time he has given public support to the US plan to create a Taliban base in the Gulf state, in which future talks could be held.
He previously rejected the idea, angry that the US and Germany had discussed potential locations without him.
The US, Germany and other countries with a stake in the decade-long war against the Taliban have increasingly been seeking a political end to the conflict.
They have argued that establishing an “address” outside the immediate region for reconciliation talks is the best way to speed up the peace process.
Earlier this month, Kabul recalled its ambassador from the Qatari capital, Doha, saying the Qataris had been discussing the issue of an office in detail with the Americans and the Germans “without keeping the Afghan government fully in the picture”.
But in a statement on Tuesday, Mr Karzai said that while he preferred the idea of Turkey or Saudi Arabia hosting the office, if the Americans wanted to locate it in Doha he would agree.
“Having an exact address for the opposition [is a condition] for practical steps toward starting negotiations,” said a statement from the presidential palace.