The Turkish military convoy with howitzers, artillery batteries and several units of the armed forces was deployed to the border district of Elbeyli in Kilis province, state news agency Anadolu reported on Monday.
Cavusoglu hit out at France's "support" of the YPG, which he said was "no secret", pointing to a meeting French President Emmanuel Macron had held on Friday with the Syrian Democratic Council, the political wing of the US-backed Kurdish Syrian Democratic Forces' (SDF).
The YPG, Syrian branch of PKK that is listed a terror organisation by Turkey, the U.S., and the European Union, has been seeking for worldwide support to prevent any possible Turkish operation against them in Syria.
Ankara views the YPG militia as a sister "terrorist" organization of the outlawed Kurdistan Workers' Party (PKK), which has waged an insurgency inside Turkey since 1984.
US -backed forces have also raised concerns about what to do with hundreds of captured IS foreign fighters.
Mevlut Cavusoglu told reporters at a briefing for domestic media that Turkey aimed to cross to the east of the Euphrates as soon as possible, the Hurriyet newspaper said, without giving further details.
Trump is making his first presidential trip to a troubled region in the wake of his recent decision to pull United States forces from neighboring Syria.
Cavusoglu will travel to Russian Federation to discuss the process of the U.S. withdrawal in the coming days, CNN Turk said.
The Kurdish militia has expressed shock at Trump's decision, and now faces a triple threat from Turkey, the Syrian government, and IS.
A committee of USA military officials will visit Turkey this week to discuss the details of the pullout with their counterparts, said Ibrahim Kalin, Turkish presidential spokesman.
It has also reiterated its determination in eliminating the YPG through military operations in eastern Syria although it said it delayed a planned strike due to the withdrawal decision of the U.S.
Reports from the region indicate other forces are also on the move as they, too, prepare for the US troop withdrawal.
Turkish officials have said that President Recep Tayyip Erdogan heavily weighed in the decision by his United States counterpart Donald Trump to pull all 2,000 American troops from Syria. A source close to SDF leadership told VOA the expectations are that Russian-backed Syrian forces will move into some of the areas the SDF vacates once the USA leaves.
Zakharova also said Moscow believes that it should be the Syrian government.
The United States has backed Kurdish fighters in northern Syria as part of an global coalition against the Islamic State jihadist group.
Erdogan's spokesman Ibrahim Kalin told reporters on Monday that a USA military delegation would arrive this week to "discuss how to coordinate [the withdrawal] with their counterparts".
Mr Abu Adel, on Tuesday said there is no sign of an imminent Turkish attack on Manbij, despite claims by Turkish-backed rebels that they are pressing ahead with an assault.