Erdogan spoke to journalists on Wednesday, following his return from talks in Russia.
He says he asked Russian President Vladimir Putin what would happen if the Syrian Kurdish fighters donned Syrian army uniforms and remained in the border area. Erdogan says Putin responded by saying he wouldn't let that happen.
Erdogan's comments were carried by Hurriyet newspaper's online edition.
The Turkish leader also says a planned visit to Washington for talks with President Donald Trump, scheduled for Nov. 13, would likely take place.
The NATO chief is calling for a political resolution to the conflict in Syria and urges Turkey to focus on the threat posed by the extremist Islamic State group, two weeks since Turkey invaded northeastern Syria in an offensive against Kurdish forces there.
Ankara considers the Syrian Kurdish fighters terrorists aligned with a Kurdish insurgency inside Turkey.
NATO Secretary-General Jens Stoltenberg said on Wednesday that "the recent developments underscore the urgent need for a political solution" in Syria.
He says it's important to ensure the extremists are defeated "and that we understand that the fight against ISIS is not over. They can come back." ISIS is another acronym for the Islamic State group.
Russia and Turkey agreed on Tuesday to deploy their forces across nearly the entire northeastern Syria border to fill the void left by President Donald Trump's abrupt withdrawal of U.S. forces.
Stoltenberg says "it is a bit too early to judge the consequences" of that agreement.
NATO defense ministers will discuss Turkey's invasion of northern Syria during talks in Brussels on Thursday.
The Kremlin has warned Kurdish fighters that they will face a renewed Turkish onslaught if they fail to withdraw their forces in line with a Russia-Turkey deal.
The warning comes a day after Russian President Vladimir Putin and Turkish President Recep Tayyip Erdogan struck a deal to share control of Syria's northeast.
Under the agreement, Turkey will hold the area it has seized in the invasion that began on Oct. 9, while Russian and Syrian troops will control the rest of the Syria-Turkey border. The deal gives Kurdish fighters 150 hours starting at noon Wednesday to withdraw from the area.
Putin's spokesman Dmitry Peskov warns that if the Kurds fail to do that, Russian and Syrian troops will step back and "the remaining Kurdish units will be steamrolled by the Turkish army."
Russian media reports say Russian military police have started patrols in northern Syria as a Turkish-Russian agreement giving Syrian Kurdish fighters 150 hours to withdraw from almost the entire northeast border region of Syria came into effect.
The Interfax agency carried a statement by Russia's military police saying patrols had begun in the northeast of the city of Manbij. Russian television meanwhile, reported a convoy of Russian troops heading toward the town of Kobane.
Under the deal, Russian and Syrian government forces were to move to ensure that the fighters pull back 30 kilometers, about 20 miles, from the border as of noon on Wednesday.
The deal reached between Turkish President Recep Tayyip Erdogan and Russian President Vladimir Putin allows Turkey to maintain control over areas it invaded this month in northeastern Syria. Ankara launched the incursion against Syrian Kurdish fighters whom it considers terrorists, claiming they are linked to a Kurdish insurgency within Turkey.
The deal gives the Russian troops and the Syrian army control over the rest of the Syria-Turkey frontier.
Turkey's foreign minister says Turkish forces will "neutralize" any remaining Syrian Kurdish fighter they come across in areas now under Turkish control in northeastern Syria.
Mevlut Cavusoglu made the comments on Wednesday — even after the military signaled it won't resume its offensive, following separate agreements Turkey reached with the U.S. and Russia.
The military said earlier the U.S. had announced Syrian Kurdish fighters completed their pullout from areas Turkey invaded this month as a five-day cease-fire expired.
Cavusoglu told Anadolu Agency: "If there are terrorist remnants, we would clear them."
Cavusoglu said the deal with Russia — which foresees joint Turkish-Russian patrols after the withdrawal of Kurdish forces — would continue until a lasting political solution for Syria is reached. He says the border areas would be locally-administered, mostly by Arabs.
He said Turkey agreed not to conduct joint patrols in the city of Qamishli, because of Russian concerns that such a move could lead to a confrontation between Turkish troops and the Syrian government forces who have long been present in the area.
Turkey's Defense Ministry is signaling it won't resume its offensive in northeast Syria, following agreements reached with the U.S. and Russia.
The ministry said early on Wednesday the U.S. had announced Syrian Kurdish fighters completed their pullout from areas Turkey invaded this month as a five-day cease-fire allowing for the withdrawal expired.
This came after the leaders of Russia and Turkey announced a separate deal for their forces to jointly patrol almost the entire northeastern Syrian border after the Kurdish withdrawal.
Under that deal, Turkey will maintain control over the areas it holds since its incursion. It also lets Russian and Syrian troops control the rest of the border.
The ministry said: "At this stage, there is no further need to conduct a new operation outside the present operation area."