It lasted more than 30 minutes, Turkish media said.
Turkish and USA authorities made a decision to meet to settle the strategic emergency between the two North Atlantic Treaty Organisation partners, Deputy Prime Minister Bekir Bozdag said on Thursday.
In a retaliatory move, Turkey's Washington Embassy also suspended non-immigrant visa services, saying, "Recent events have forced Turkish Government to reassess the commitment of the Government of the United States to the security of Turkish Mission facilities and personnel".
In response, Turkey's Embassy to the US suspended non-immigrant visa services in the USA, citing security concerns. Tillerson expressed his "profound concern" about the arrests, the US State Department said in a statement.
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U.S. Defense Secretary Jim Mattis said the dispute has not affected the U.S. military's relationship with Turkey's armed forces.
The spat between the two countries was ignited by the recent arrest of Metin Topuz, a Turkish employee at the US consulate in Istanbul, over suspected link to the USA -based Muslim cleric Fethullah Gulen, who is accused by Ankara of being behind a failed coup attempt in July 2016.
Bozdag said Turkish and US diplomats would meet in the next few days.
U.S. -Turkish relations were already strained over U.S. military support for Kurdish fighters in Syria and the United States' unwillingness to extradite Muslim cleric Fethullah Gulen, a former Erdogan ally whom Ankara views as the mastermind behind last year's failed military coup.