Hours after Ankara announced officials would meet soon to settle differences, Erdogan accused the US consulate in Istanbul of hiding an individual with links to a network he blames for last year's failed coup.
Wednesday's telephone call between Tillerson and Turkey's top diplomat Mevlut Cavusoglu came after the US ambassador to Turkey said Tillerson held talks to try and resolve a major diplomatic break between the two North Atlantic Treaty Organisation allies.
Ties between the two countries are tense over Gulen, who is wanted in Turkey but who denies allegations of plotting the failed coup.
Turkey felt many allies were slow to condemn the coup attempt and failed to appreciate the danger it faced.
Ankara and Washington are going through their worst bilateral crisis in years after U.S. Istanbul Consulate official Metin Topuz was arrested last week, prompting the U.S.to announce on October 8 that it has stopped issuing non-immigrant visas in Turkey.
The Turkish government's crackdown on Gulen's followers in Turkey has led to the arrests of more than 50,000 people for alleged links to terror groups.
Secretary of State Rex Tillerson told Turkey's foreign minister that the Trump administration is profoundly "concerned" about the detention of USA citizens and the arrest of local Turkish consular employees, the State Department said.
Ambassador Bass told reporters on Wednesday the United States government had still not received any official explanation from the Turkish government for why the employee was arrested.
Turkish Foreign Minister Mevlut Cavusoglu spoke on the phone with his U.S. counterpart Rex Tillerson on Wednesday to discuss mutual visa suspension issue, a Turkish foreign ministry source said, APA reports quoting Anadolu Agency.
"Let me be very clear, the person who caused this is the ambassador here. It is unacceptable that the U.S. has sacrificed a strategic partner like Turkey to a presumptuous ambassador", he said.
Turkey's presidential spokesman Ibrahim Kalin said Thursday that Turkey has received a request from the U.S.to resolve the ongoing visa spat.
"On the one hand you say you are the capital of democracy, but you hide PKK and FETO members", Erdogan said, using the label his government has given to Gulen's network.
"Turkey is not doing arbitrary arrests".
Ambassador Bass said this week no one was hiding in the USA consulate, and that he had seen nothing of merit in the charges against the pastor, Andrew Brunson.
Another consular employee was detained earlier this year and Turkish officials have said they want to question a third.
He said Turkey would abandon its plans to supply US -made weapons to its police force.
"If an ambassador in Ankara is governing the United States, it is a shame", he added.
Erdogan blames United States envoy for visa dispute, calling on Washington not to sacrifice alliance for "impertinent ambassador". "Someone should have said: "You cannot treat your strategic partner this way, you can't behave like this".