Turkish President Recep Tayyip Erdogan addresses his supporters next to his wife, Emine Erdogan, during a rally Sunday in Bursa, Turkey. (Handout/Reuters)

Turkey on Sunday opened a new front in its assault on Kurdish militias in northern Syria, launching a ground offensive with allied Syrian rebels and injecting new uncertainty into an already volatile civil war.

The land operation by Turkish forces, which began Sunday morning, comes as Turkey intensified air and artillery strikes over the weekend on the Syrian Kurdish enclave Afrin.

Turkey on Saturday had announced the formal start of "Operation Olive Branch," an apparently open-ended offensive that envisions attacks on at least two Kurdish-controlled cities. Turkish troops and Syrian rebels would then establish a "secure zone" along the border, the Turkish prime minister said Sunday.

"Our units have entered Afrin . . . with the Free Syrian Army," Prime Minister Binali Yildirim told reporters in Istanbul, according to Turkey's Hurriyet newspaper. "This means the land operation has begun."

Also Sunday, rockets fired from northern Syria hit the Turkish town of Reyhanli, killing one and injuring 32, officials said.

The militia group YPG, which controls Afrin, said six civilians and three fighters had been killed in the strikes overnight. Syrian Kurdish officials denied that Turkish troops had crossed into Afrin, claiming instead that YPG fighters had repelled an attack.

But the threat of a full-blown ground invasion also gave fresh urgency to the fighting and raised questions about the military and political objectives of the offensive.

"It's tough to know exactly what the Turks are doing because the geographic scope and aims are not clear," said Sam Heller, a fellow at the Century Foundation.

Turkish officials have portrayed the assault as linked to their battle with Kurdish separatists at home and say that Syrian Kurdish militias are indistinguishable from the Kurdistan Workers' Party, or PKK, which has waged a decades-long guerrilla war in Turkey's southeast.

"The military operation in Afrin aims to liberate the area by eliminating the PKK-YPG-linked administration," a Turkish official said late Saturday. He spoke anonymously to discuss the military operations.

Turkey and allied rebels also plan to "rebuild" local institutions and infrastructure, the official said, including in Afrin and in Manbij to the east.

"They could get bogged down in Afrin if they meet very determined resistance," Heller said of Turkish forces and their allies. "It's also conflict that could spread elsewhere," including Turkey itself, he said.

Kurds throughout the region have long aspired to independence or self-rule. Amid the chaos of Syria's years-long war, Kurds there seized and administered territory. And for the United States, they eventually emerged as the most effective partner in the fight against the Islamic State.

As a result, the Turkish operation threatens to further degrade relations between Ankara and Washington, which have become strained over the course of the war.

The State Department on Sunday said, "The United States is very concerned about the situation in northwest Syria."

"We urge Turkey to exercise restraint and ensure its operations remain limited in scope and duration . . . to avoid civilian casualties."

Ahead of the Turkish operation, U.S. officials called on Turkey to focus instead on eradicating Islamist militants. Turkey, a NATO ally, has accused the United States of aiding "terrorists" in Syria.

The operation "continues to ensure peace and security for our people, protect Syria's territorial integrity and eliminate all terrorist elements in the region," Ibrahim Kalin, a spokesman for Turkish President Recep Tayyip Erdogan, said Sunday on Twitter. "Turkey expects its allies to support its fight against terrorism in all of its forms."

On Sunday, both Iran and Egypt condemned the Turkish offensive. Egypt blasted the operation as a violation of Syria's sovereignty. According to the Associated Press, Turkey's chief of staff, Gen. Hulusi Akar, discussed the offensive with his Iranian counterpart on Sunday.

Loveluck reported from London. Suzan Haidamous in Beirut contributed to this report.