Syrian civilians flee Afrin on March 12 amid battles between Turkish-backed forces and Kurdish fighters. (Stringer/AFP/Getty Images)

Turkish forces and allied rebels announced the encirclement of the Syrian city of Afrin on Tuesday in a major escalation of a weeks-long offensive to oust Kurdish militants from the area.

“The city center of Afrin was besieged and critical areas for subsequent operations have been seized,” the Turkish Armed Forces said, adding that the offensive “continues successfully as planned.”

A Britain-based monitoring group, the Syrian Observatory for Human Rights, confirmed that Turkish troops and their Syrian rebel proxies had surrounded the city. Kurdish officials, however, downplayed the reports, saying that only parts of the city were besieged.

The renewed push follows rapid advances by Turkish-backed rebels against Kurdish militants in recent days, after nearly two months of fighting in difficult and hostile terrain.

The advances also come as U.S. and Turkish officials have taken strides to repair relations damaged by the operation and by U.S. cooperation with Syrian Kurds more broadly. The United States has worked closely with Kurdish fighters — known as the YPG — to battle Islamic State militants in Syria. But Turkey, which is fighting Kurdish insurgents at home, says Kurdish-controlled territory in Syria is a threat to its national security.

The Turkish operation seeks to establish a buffer zone patrolled by its proxies inside Syria, officials have said.

While much of the territory taken so far has been sparsely populated, Afrin city is a dense urban environment. Rights groups point to the potential for high civilian casualties if the battle reaches residential areas.

Afrin, which had a majority Kurdish population prior to the breakout of Syria's civil war, has been under Kurdish control since 2012 when Syrian government forces were ousted. The YPG, which formed to protect Kurdish residents amid the chaos of the war, controls two other enclaves in Syria, which the group had hoped to assemble as the foundation for a potential future state.

“The offensive is now pushing ever closer toward the city with its large civilian population,” United Nations Secretary General António Guterres told the U.N. Security Council on Monday.

A report Tuesday from the U.N. Office for the Coordination of Humanitarian Affairs said that “supply routes have been disrupted’ in Afrin as a result of the bombardment and that civilians inside the city are “seeking refuge in basement accommodation.”

A spokesman for the YPG in Afrin, Brusk Haska, said that Turkish forces were targeting the only road open for humanitarian aid with artillery and airstrikes. Turkey denies targeting civilian infrastructure.

Another Syrian Kurdish official, Newaf Xelil, said that Kurdish forces would “evacuate the elderly and civilians” if necessary as the fighting intensified. “A mass evacuation is unlikely,” he said. The U.N. on Tuesday also said that local authorities appeared to be “preventing large scale movement of civilians out of the district.”

Also Tuesday, Turkish Foreign Minister Mevlut Cavusoglu told Turkish reporters that the United States and Turkey would decide soon on a process for relocating Kurdish forces from the Syrian city of Manbij, about 90 miles east of Afrin. The YPG helped oust the Islamic State from the city in 2016 with U.S. backing.

Turkey had previously threatened to attack Manbij as part of its wider bid to eject Kurdish forces from parts northern Syria. U.S. forces are stationed at Manbij to thwart any counteroffensive by Islamic State militants.

Amid tension over U.S. ties with the Syrian Kurds, U.S.-Turkish relations have plunged to their lowest point in years. U.S. and Turkish officials have recently set up working groups to address their differences and hammer out details of cooperation in northern Syria.

“Both sides recognize that there is going to be compromise here,” a European diplomat said of the United States and Turkey. The official, who works on Syria, requested anonymity because he was not authorized to speak publicly about the crisis.

“The U.S. is not going to forsake the YPG as an ally,” the diplomat said. “But the Turks don’t like to see the YPG . . . operate in areas where they consider it appropriate.”

Habib reported from Stockholm. Zakaria Zakaria in Istanbul and Louisa Loveluck in Beirut contributed reporting.