Erdogan said Turkey no longer regarded ambassador John Bass as the US representative to Turkey after American missions in the country stopped issuing visas.
The dispute erupted last week when Turkey arrested a Turkish employee of the American consulate on suspicion of links to the group blamed for last year's failed coup.
In response, the United States stopped issuing non- immigrant visas from its missions in Turkey, prompting Turkish missions in the United States to hit back with a tit-for-tat step of their own.
"We do not see him as the representative of the United States in Turkey."
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Bass is shortly to leave Turkey after being nominated the US envoy to Afghanistan and it is traditional for outgoing envoys in Turkey to make valedictory visits to top officials.
Although Bass is in Turkey for only a few more days, it is unprecedented in the history of Turkish-US relations for Ankara to say it no longer recognises Washington's ambassador.
Some Turkish officials have long alleged a US hand in the coup attempt on July 15 last year, which Ankara blames on the US-based Muslim preacher Fethullah Gulen.
Washington has dismissed claims it was involved as a ludicrous conspiracy theory and Gulen himself denies any link to the plot.
"The US should evaluate one thing: how did those agents leak into the consulate?" Erdogan said.
The US embassy has dismissed the allegations against the arrested consulate staffer as baseless.
The man is reportedly in hiding at the consulate but the Turkish authorities yesterday detained his wife and his son, and today detained his daughter.
In March, a Turkish employee at the US consulate in the southern city of Adana was arrested on charges of supporting the Kurdistan Workers' Party (PKK).
"The current crisis is unlikely to be de-escalated with ease," said Anthony Skinner of Verisk Maplecroft, a risk consultancy.
Turkish officials had expressed hope of a new page in Ankara-Washington relations under President Donald Trump after repeated bickering in the last months of Barack Obama's term.
He said that if the order to suspend visa issuance came directly from Bass, then the US administration "should not keep him here one more minute".
"They need to ask him, How can you break relations between the United States and Turkey, who gave you this authority?" he said.
Turkish Prime Minister Binali Yildirim rejected American criticism over the arrest of US consulate staffers, saying Ankara did not need Washington's approval for such moves.
Pro-government media have rounded on the United States, with the Yeni Safak daily describing the US as "not an ally but an enemy".
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