The Turkish government should allow US embassy staff it detained access to attorneys, US Department of State spokesperson Heather Nauert said during a press briefing on Tuesday.
The second arrest at the Istanbul consulate last week led to the US announcing on Sunday it had halted issuing non-immigrant visas in Turkey - a move reciprocated within hours by Ankara.
"We have not agreed and are not agreeing to this ambassador making farewell visits with ministers, the parliament speaker and myself", Erdogan said of United States ambassador John Bass, who is shortly to leave Turkey after being nominated the U.S. envoy to Afghanistan.
"We have not agreed and are not agreeing to this ambassador making farewell visits with ministers, the parliament speaker and myself", Erdogan said.
The US mission in Turkey and subsequently the Turkish mission in Washington mutually reduced visa services after a locally-hired US mission employee was detained in Turkey last week.
On Thursday, the US Embassy in Turkey said that the charges against Topuz were baseless and undermined partnership between Washington and Ankara.
Yildirim said the dispute should be resolved as soon as possible, but defended Turkey's arrest of a U.S. consulate employee.
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The president of the Turkish-American Business Council, Kamil Ekim Alptekin, said that the two states needed each other politically and economically, and "we want to solve the problems without their reflection on economic relations, but if it affects national security, no country can make concessions".
"Above all, the decision is very upsetting".
Within hours Turkey announced it was taking the same measures against US citizens.
"If you have a valid visa, you can still travel to the United States".
"In terms of bilateral relations between Turkey and the USA, we have now hit rock bottom".
According to Turkish media, Metin Topuz has been accused by the country's authorities of undermining the constitutional order, espionage and an attempt to overthrow the Turkish government.
The Turkish foreign ministry last week said the U.S. has no grounds to protest the arrest.