Turkey considers the People's Protection Units (YPG), in Syria a terror organisation and an extension of the Kurdistan Workers' Party (PKK), which has waged a three-decade-long insurgency against the Turkish state.
Speaking in Istanbul, President Recep Tayyip Erdogan criticised the US decision to ally with "terror organisations" for the long-awaited operation to capture Raqqa, the de facto capital of ISIS.
"We said we would not be in such an operation with you where you ally with terror organisations and so we said good luck," Erdogan said.
He said he warned Trump that Turkey would combat YPG if the group posed any security threat. "We are already telling you in advance, our rules of engagement give us this authority, we will take such a step and we won't discuss it or consult with anyone. Because we have no time to lose," he said.
Citing a cross-border offensive Turkey launched against ISIS and the YPG in Syria in 2016, Erdogan said "we won't hesitate to launch similar operations if we see the need."
Earlier on Thursday, Foreign Minister Mevlut Cavusoglu said the Trump administration understood Turkey's position against the YPG. "They did not say anything negative about this issue and treated it with understanding," he said.
In April, the US had criticised Turkish airstrikes against Kurdish militants in Syria and Iraq.
Cavusoglu said Trump's administration seems more understanding about Turkey's security concerns. He went on to plead for the replacement of Brett McGurk, the US presidential envoy for the global coalition against ISIS.
"This McGurk is definitely supporting the PKK and YPG. It would be beneficial for this person to change," he said, accusing the diplomat of carrying on Obama-administration policies.
Cavusoglu said Turkey received US assurances that arms sent to the YPG would be used only against ISIS, without explaining how this would be monitored.
"The weapons provided will only be used in Raqqa and its south, they will absolutely not be used against Turkey, this will not be allowed," Cavusoglu said. "Turkey and the US will together run an active combat against the PKK."
A cease-fire between Turkey and the PKK collapsed in July 2015 after a two-and-a half year hiatus in fighting, leading to clashes in Turkey's southeast and round-the-clock curfews as well as airstrikes on alleged PKK camps in northern Iraq.
According to the International Crisis Group, at least 2 798 people, including state security personnel and Kurdish militants, have been killed in Turkey. The death toll includes nearly 400 civilians.
The PKK is considered a terror group by the US and Turkey's Western allies.