On Monday Ankara sent more troops to its Syrian border and said an offensive targeting the Syrian Kurdish People's Protection Units (YPG) militia and IS group will be launched in the coming months.
Turkey views the YPG as a "terrorist offshoot" of the outlawed Kurdistan Workers' Party (PKK), which has waged an insurgency against the Turkish state since 1984.
But the militia has also been a key US ally in the fight against Islamic State in Syria, working with American forces on the ground there.
"Just as we did not leave our Syrian Arabs to Daesh (IS), we will not leave Syrian Kurds to the cruelty of the PKK," Erdogan said during a speech in Ankara.
A Turkish military convoy arrived overnight on Monday at the border with local media reporting that some vehicles had entered Syria.
In a telephone conversation Sunday between Trump and Erdogan, which both sides described as "productive", they agreed to avoid a power vacuum in Syria after the US withdrawal.
"President Erdogan invited President Trump to visit Turkey in 2019. While nothing definite is being planned, the President is open to a potential meeting in the future," a White House spokesperson later said on Monday evening.
Erdogan's spokesman Ibrahim Kalin told reporters on Monday that a US military delegation would arrive this week to "discuss how to coordinate (the withdrawal) with their counterparts".
A Turkish foreign ministry delegation would go to Washington for talks early January, he added.
Trump stunned the US political establishment and allies last week with his decision, days after Erdogan had warned that Ankara would soon launch an offensive in northern Syria.
Reporter's code: 50101