Karzai reacted furiously to the office being styled as a Taliban government-in-exile under the rebels' white flag and using the formal name of the "Islamic Emirate Of Afghanistan" from their hardline 1996-2001 regime.
The opening of the Qatar office last Tuesday was intended as a first step towards a peace deal as the US-led NATO combat mission winds down 12 years after the Taliban were ousted after the 9/11 attacks.
A statement from the US embassy said that Dobbins and Karzai would discuss "the reconciliation process which President (Barack) Obama and President Karzai agreed is the surest way to a lasting peace".
Kabul, which said it was still committed to the peace process, insisted the Qatar office must only be used for direct negotiations between the Taliban and the Afghan government.
"After these meetings (with Dobbins), our information will be complete and we can then decide whether to send our delegation to Qatar," Ismael Qasimyar, a senior member of the Afghan peace negotiators, told AFP.
Dobbins, a veteran diplomat who re-opened the US embassy after the 2001 fall of the Taliban, is also likely to try to revive separate talks on an agreement that would allow Washington to maintain soldiers in Afghanistan after next year.
Karzai, who has so far refused to send representatives to Qatar, broke off negotiations on the Bilateral Security Agreement (BSA) in reaction to the Taliban office.
Mohammed Naeem, a Qatar-based spokesman for the Taliban, said Monday that the flag and sign unveiled at an opening ceremony had been agreed with Qatar -- but not with the United States.
About 100,000 foreign combat troops, 68,000 of them American, are due to withdraw by the end of 2014, and NATO formally transferred responsibility for nationwide security to Afghan forces last week.
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