Turkey's targeting of the YPG, which it views as a security threat, has opened a new front in Syria's multi-sided civil war.
Three new campsites were being set up northeast of Afrin near Syria's Azaz region, where most refugees are expected to head.
"Those who support the terrorist organization will become a target in this battle", Bekir Bozdag said.
"We have always been emphasizing that the United States has embarked on creating alternative bodies of power on a significant part of Syrian territory", Sergey Lavrov said at a press conference held in Moscow on Monday.
The YPG have been armed by the United States as part of the broader fight against the so-called Islamic State.
A North Atlantic Treaty Organisation statement said Turkey has suffered from terrorism and has the right to self-defense but urged Ankara to do so in a "proportionate and measured way", the Associated Press reported.
The letter indicated that there are more than 200 Christian families living in Afrin, which is an isolated part of the Syrian federation bordering areas controlled by Islamist rebels and the regime of Syrian President Bashar al-Assad.
The United States should "stop supporting terrorists" if it wants to avoid a possible confrontation with Turkey in Syria, Deputy Prime Minister Bekir Bozdağ said on January 25.
"We experienced war once in Syria, and we don't want it here", Ahmar added.
"Regarding our position on an invitation - if it happens - we will not attend the congress in the light of this barbaric, occupation aggression on Afrin", Jia Kurd said.
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Shervan Derwish, a spokesman for the Manbij Military Council, said his forces are on "full alert" in case Turkey moves on the city, where US-led coalition forces are still present.
But, in a telephone call with Erdogan, US President Donald Trump urged the Turkish leader to "avoid any actions that might risk conflict between Turkish and American forces" and emphasized the "shared goal" of the lasting defeat of the Islamic State terrorist movement, White House spokeswoman Sarah Sanders said in a statement.
However Turkey has disputed that characterisation of the conversation.
In a speech in Ankara on Thursday Yildirim again slammed the United States for backing the Syrian Kurdish militia force instead of standing by a North Atlantic Treaty Organisation ally.
But Turkish president Recep Tayyip Erdogan vowed on Wednesday to expand "Operation Olive Branch" toward the Kurdish enclave of Manbij, some 60 miles (100km) east of Afrin.
They appear to have made only limited gains, hampered by rain and clouds, which have limited the air support.
The Syrian Observatory for Human Rights, a Britain-based group that monitors the civil war, reported airstrikes in almost 20 villages.
Erdogan's office said the Turkish leader urged Trump in the phone call to halt the U.S. supply of weapons to the Syrian Kurdish militia.
Turkey considers the YPG to be the Syrian arm of the Kurdistan Workers' party (PKK), a designated terror group that has fought a decades-long insurgency against the Turkish state.
The deputy prime minister noted that if Washington does not want to spoil relations with Ankara, then the U.S. should stop arming PYD and YPG terrorists.
On the sidelines of the assembly of foreign ministers' meeting, which was held in Paris on Tuesday, Cavusoglu met U.S. Secretary of State Rex Tillerson.