Afrin is controlled by a Syrian Kurdish militia known as the YPG.
"We expect from our allies that they behave in accordance with the spirit of our deep-rooted relationship during this process", Erdogan said, adding "despite everything" he hoped for cooperation to achieve "common interests" in the region.
Turkey, however, considers the Kurdish forces as an extension of the Kurdistan Workers' Party, which is considered a terrorist group by Turkey, the US and the European Union, according to Reuters.
Erdogan has repeatedly said that Afrin should be cleared of "terrorists" and in November 2016, he said Turkish troops needed to be deployed there.
Turkish security forces conducted shelling of Syria's northern Aleppo province targeting forces of the Syrian Kurdish Democratic Union Party (PYD), Sputnik reported citing local media. About half the force will be SDF veterans, and recruiting for the other half is under way, the Public Affairs Office said.
Erdogan's spokesman Ibrahim Kalin said that Washington "is taking worrying steps to legitimise this organisation and make it lasting in the region".
He also said Turkey could drive YPG forces out of Manbij.
Washington opposes those autonomy plans, even as it has backed the SDF, the main partner for the USA -led coalition against Islamic State in Syria.
The coalition said the Border Security Force would operate under SDF command and that around 230 individuals were now undergoing training in its inaugural class. Therefore, the ethnic composition of the force will be relative to the areas in which they serve.
The Kurdish YPG militia said Turkish forces inside Syria fired shells into Afrin on Saturday, but no one was wounded. YPG played in a prominent role in defeating the group in its former de facto capital in northern Syria late a year ago.
IED stands for improvised explosive device.
Turkey was a major supporter of rebels fighting to overthrow Syria's President Bashar al-Assad, but is alarmed by the strength of Kurdish forces - which Ankara says are linked to Kurdish militants fighting in southeast Turkey. A senior Syrian Kurdish politician said last week that the USA appeared in no hurry to leave Syria.