(CNN) Turkey's Prime Minister warned that Kurdish YPG forces will pay "twice as much" following the deaths of seven Turkish soldiers in Syria's Afrin province.

Prime Minister Binali Yildirim made the threat in a tweet Saturday, Turkey's state media said. Saturday marked Turkey's deadliest day in its military operation dubbed "Operation Olive Branch" in northern Syria.

Turkish forces entered the Afrin area in an attempt to drive US-backed, Syrian-Kurdish YPG militia from the area last month.

Five Turkish soldiers were killed Saturday when a tank was destroyed by a missile in Sheikh Haruz, northeast of Afrin, Turkish state media reported.

Turkish armed forces said a sixth soldier was killed near the border town of Kilis, and another died in an undisclosed location fighting militia forces, Anadolu reported.

'Operation Olive Branch'

Turkey launched "Operation Olive Branch" on January 20 with the aim of ending the US-allied militia control of Afrin and the surrounding region along the Syrian-Turkish border. Turkey has long wanted to establish a safe zone: a 19-mile-wide strip of land in Syria along the border that Turkey helps control.

In Ankara's eyes, Syrian Kurds are virtually indistinguishable from Kurdish separatists in Turkey, a group it has long considered terrorists. The Kurdish YPG control a large chunk of northern Syria, so a safe zone would create a buffer along the border.

The Turkish military has also dropped leaflets into Afrin this week, according to sources on the ground and the Turkish military. The leaflets, written in Arabic and Kurdish, urge the residents of Afrin to cooperate with the Turkish military operation.

"It is time to end violations and oppressions of the terrorists, PKK (Kurdistan Workers' Party), PYD, YPG and ISIS," the leaflets say. The PYD is described by the Central Intelligence Agency as PKK's Syrian wing.

"These groups have attacked their neighbors with weapons and destroyed mosques... Our dignified brothers, don't let the terrorists use your children , destroy your homes and your future... It is time to say enough to the terrorists..."

The risk to US relations

Turkey's high-stakes incursion in Afrin risks inflaming tensions even further with its NATO ally, the US, which is funding the very group Turkey is trying to defeat, the Kurdish YPG, in the fight against ISIS.

Shortly after their assault began, Turkish forces said they had killed 260 Kurdish and ISIS fighters in the region. The claim can't be independently verified, and CNN has no indication there are ISIS fighters in the area that Turkey is fighting.

Speaking with Turkish President Recep Tayyip Erdogan by phone, US President Donald Trump talked tough, saying Turkey's "Operation Olive Branch," targeting the US-backed Kurdish fighters, risked undercutting shared goals in Syria, according to the White House. Trump warned Erdogan against escalating military action in the region. Turkish officials immediately disputed that account of the call, saying the two leaders simply exchanged views on the situation.

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Erdogan has also slammed the US plan to back a border protection force for Kurds in northern Syria in an effort to train and equip them to keep ISIS from coming back in, calling the effort "building an army of terror," according to Turkish state media.

A call for cooperation

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Turkish presidential spokesman Ibrahim Kalin t old CNN their operation isn't against the Kurds of Afrin or Syria.

"This is an operation against a terrorist network that claims to represent the Kurds, which is far from the truth," he said.

Kalin cited Amnesty International in pointing out that the PYD/YPG has committed war crimes by razing villages and forcibly removing local communities from their native lands.

He said the operation aims to remedy the situation and facilitate the return of Syrian refugees to their country.

"The primary goal of the operation is to clear Syrian territories of all terrorist groups," he explained, saying Turkey has fought against ISIS and cooperated with its allies in eliminating ISIS terrorists. "It is deadly wrong to think that the PKK does not pose a threat to Western countries and therefore should be seen as Turkey's problem."