US Secretary of State Mike Pompeo said Monday that talks were under way on Washington's proposal to establish a "safe zone" in flashpoint border areas of northeastern Syria, where tensions are rising between Turkey and Kurdish militia.

"We want to make sure that the folks who fought with us to down the (Islamic State group) have security... and also that terrorists acting out of Syria aren't able to attack Turkey," Pompeo said.

"We want a secure border for all the parties," he said in the Saudi capital Riyadh, the latest leg of a whirlwind Middle East tour.

Washington is holding talks with all relevent sides about such a "safe zone", he added.

His comments came a day after US President Donald Trump in a tweet pushed for the creation of a 30-kilometre "safe zone", without saying who would create, enforce or pay for it.

Trump also did not say exactly where such a buffer area would be set up.

Turkish Foreign Minister Mevlut Cavusoglu on Monday said his country was "not against" a "security zone" in Syria.

Tensions have been high between the United States and Turkey over the fate of Washington's Syrian Kurdish allies in the fight against the Islamic State group.

Ankara has repeatedly threatened a new cross-border operation against the Kurdish People's Protection Units (YPG), which have been working closely with the US in the war on IS jihadists.

Turkey views the YPG as a "terrorist offshoot" of the outlawed Kurdistan Workers' Party (PKK), which has been waging an insurgency against the Turkish state since 1984.

Turkish President Recep Tayyip Erdogan's spokesman Ibrahim Kalin on Monday said Ankara would "continue to fight against them all", referring to IS and the YPG.

His comments came after Trump, in Sunday's tweet, warned Turkey of economic devastation if it attacks the Kurds in the wake of a US pullout from Syria.

On Sunday Trump also urged the Kurds not to "provoke" Ankara.

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