The US move was in response to the arrest of a US consulate staffer accused of having links to the group of US-based preacher Fethullah Gulen...
The US and Turkish embassies in Ankara and Washington announced on Monday they would start processing visa applications for each other's citizens after an almost month-long suspension.
"The resumption of visa services, even if limited, is a positive step," Yildirim said during a press conference at Ankara airport before he was due to fly.
He will meet with Vice President Mike Pence during the visit expected to last until Friday.
The diplomatic row began after the US decided to stop handing out visas in Turkey from October 8, which was followed almost immediately by a tit-for-tat move by Ankara to stop issuing Turkish visas for Americans.
The US move was in response to the arrest of a US consulate staffer accused of having links to the group of US-based preacher Fethullah Gulen. The employee remains in custody.
Ankara blames Gulen for last year's failed coup against President Recep Tayyip Erdogan, charges the preacher strongly denies.
The US embassy in Ankara said it resumed visa services after the Turkish government gave "assurances" that no other US mission employee in Turkey was under investigation and that Turkey would inform the US in advance if further arrests were made.
But the Turkish embassy in Washington said late Monday it could not provide "any assurances regarding files that are subject of ongoing legal processes".
Yildirim said it would "not fit with the principles of the rule of law" to either give or ask for such reassurances.
Several American citizens are in custody in Turkey including pastor Andrew Brunson, who ran a church in the western city of Izmir.
He has been held since October 2016 on charges of being a member of Gulen's group.
Turkey continues to call for Gulen's extradition, a bone of contention between the NATO allies and a subject Yildirim again brought up.
"Everything has been done for the extradition," Yildirim said, referring to files sent to the US.
He added that Turkey expected the US judiciary to start legal proceedings against Gulen.