"This situation must come to an end as it is not a sustainable situation," said Deputy Prime Minister Bekir Bozdag, who is also government spokesman.
"It will be in the interest of both countries for the visa crisis not to be extended further."
The American delegation will meet Turkish officials from the foreign, justice and interior ministry on Tuesday, Bozdag told reporters in Ankara.
Last week relations plunged between the NATO allies after Washington stopped issuing non-immigrant visas at its missions in Turkey following the arrest of a US consulate employee over alleged links to the group accused of launching last year's failed coup.
Turkey responded with a tit-for-tat measure and President Recep Tayyip Erdogan last week blamed outgoing US ambassador to Ankara John Bass for the suspension.
"Turkey-American relations have passed very strong tests, but we have never faced such incidents like the visa crisis in any period," Bozdag said.
Jonathan Cohen, Deputy Assistant Secretary for European and Eurasian Affairs, is leading the American delegation, state-run news agency Anadolu said.
Turkish officials had long expressed the hope of improving Ankara-Washington ties under US President Donald Trump, after they eroded badly during the final months of Barack Obama's administration.
The two countries have been at odds over US support for the Syrian Kurdish militia fighting the Islamic State extremist group in northern Syria and the failure to extradite Pennsylvania-based Muslim cleric Fethullah Gulen.
Ankara accuses Gulen, who has lived in self-imposed exile since 1999, of ordering the attempted overthrow of Erdogan, charges which he strongly denies.
Erdogan and other Turkish officials have been careful not to blame Trump for the latest straining of ties.
Last month Trump gave the Turkish leader "high marks" for "running a very difficult part of the world".
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