It is Yildirim's first visit to the U.S.as Turkish premier and he is accompanied by Deputy Prime Minister Mehmet Simsek, Foreign Minister Mevlut Cavusoglu and Energy Minister Berat Albayrak.
On Thursday, Yildirim is due to meet United States Vice President Mike Pence before travelling to NY, where he will meet the UN Secretary General Antonio Guterres and representatives of the Jewish community in NY before addressing investors at dinner.
The diplomatic row began after the USA chose to stop handing out visas in Turkey from October 8, which was followed nearly immediately by a tit-for-tat move by Ankara to stop issuing Turkish visas for Americans.
USA missions in Ankara and Istanbul announced that they have resumed limited processing of all non-immigrant visa services, with priority to special cases.
Turkey said it would match the move, relaxing a visa ban of its own that was instituted last month in retaliation against Washington.
U.S embassies and consulate said in the official website, "We have received initial high-level assurances from the Government of Turkey that there are no additional local employees of our Mission in Turkey under investigation".
It also said a reference to the security conditions of USA missions in Turkey in the US embassy's statement was "considered odd" and did not reflect the truth. Gülen is now in the United States, in exile from Turkey. Ankara also maintains that organic branches of the PKK, such as the PYD in Syria should also be treated as such, often leading to tensions between Turkey and the US.
Ankara has complained of Washington's slow pace in processing the request since the attempted putsch in July 2016, although a decades-old extradition treaty exists between the two NATO allies.
Noting that the leader of the Gülenist Terror Group (FETÖ), which is behind last year's botched July 15 coup attempt, must be extradited as soon as possible, the prime minister said both countries should work to achieve normalized bilateral relations and focus on the future of ties. However, Yildirim reiterated Turkey's stance that it had not offered assurances to Washington.
Prominent US diplomats and think tank representatives were in attendance at the meeting, which was closed to the press.