Turkish president Recep Tayyip Erdogan has promised to convince Mr Trump to reverse his administration's decision to arm the YPG when the two leaders meet at the White House next week.
Syrian opposition activists and media say Kurdish-led forces are closing in on the de-facto capital of the Islamic State group in Syria, seizing a cotton factory only a couple of miles north of the city.
The US-backed Syrian Democratic Forces (SDF) had independently cut a deal with the militants that let a group of about 70 of them leave Tabqa, a strategic city by a dam near the militant group's headquarters in Raqqa.
The announcement on Friday followed US President Donald Trump's decision on Monday to approve direct arms shipments to the SDF's Kurdish elements - the Kurdish People's Protection Units (YPG) - to "ensure a clear victory" over ISIL.
Tens of thousands of people living in besieged areas around Damascus, Homs and Aleppo - Syria's largest city - have surrendered under similar agreements in recent months, agreeing to relocate in what critics have said amounts to forced displacement.
But the battle to capture the area can not happen until the Kurds receive heavy weapons from the United States military, according to the Syrian Democratic Forces commander. The YPG is the main component of the SDF.
Angered by a USA decision to arm Kurdish YPG fighters in Syria, Turkey's President Tayyip Erdogan heads to Washington this week for talks with Donald Trump seeking either to change the president's mind or to "sort things out ourselves".More news: Brazil Lifts Public Health Emergency as Zika Cases Drop
The spat over Syria represents the deepest crisis in bilateral ties since Ankara denied Washington permission to deploy U.S. troops to attack Iraq from Turkish soil in 2003.
But a face-to-face confrontation on the matter between Trump and Erdogan seems inevitable.
"I believe this support will arrive soon", he said.
There are risks to arming the YPG.
The Turks fear any weapons the US provides the Syrian Kurds could well end up with their ethnic brethren in Turkey, who've fought violently as part of a separatist insurgency for more than three decades.
"We have suggested other solutions", Yildirim said, speaking to reporters at an event in London.
Erdogan's visit comes amid rising tensions with Turkey.More news: Atletico Madrid v Real Madrid
"Erdogan has very few cards to play", says Emre Uslu, a Turkish journalist who fled his country in 2014 and has been teaching at Virginia International University in Fairfax, Virginia, near Washington.
But one crucial steppingstone in the campaign to oust the militant group from Raqqa was finally reached Tuesday, when President Donald Trump chose to arm Syrian Kurdish fighters poised to move in on the northern Syrian city.
In April 2017, US President Donald Trump termed the massacre of Armenians in 1915 "one of the worst mass atrocities of the 20th century". "One terrorist organization can not be destroyed by another terror organization", premier Binali Yildirim told reporters about his brief meeting Thursday with U.S. Defense Secretary James Mattis in London at conference on Somalia.
Erdoğan's trip to Washington will also be a moment for him to lobby for the extradition of Fethullah Gülen, a cleric the Turkish government claims orchestrated the failed coup of 2016.
"We do not supply weapons to them and they do not particularly need our supply".
They are backed by coalition air strikes, USA special forces advisers, and even an American Marines artillery battery. If that is the case, then we will respect that.More news: Indian diplomat's phone seized in Islamabad court