BEIRUT, LEBANON — Syrian government forces made significant progress Monday in recapturing Homs from the rebel forces that have held the country's third largest city for more than a year, according to rebel commanders and military officials in neighboring Lebanon.

In its 10th day, the siege began by pounding the rebel-controlled Old City and Khaldiyeh neighborhoods with airstrikes and artillery before ground units began to advance slowly into the dense urban maze where rebels have been preparing defenses for months.

"The vicious campaign has been going on for nine days and the regime has entered into parts of Khaldiyeh, but the aim is to take over all of Homs," said Abu Rami, a rebel activist with close ties to the rebel factions under siege.

Attempts to contact Syrian officials about the offensive either failed or were ignored.

Homs has been a symbolic and strategic asset to both sides since it became one of the first major cities in Syria to have several neighborhoods wrested from regime control. It lies at a crucial crossroads between the capital, Damascus, and the coast, home to Syria's ports and ethnic villages that are home to supporters of President Bashar Assad.

The city's proximity to Lebanon has helped drag Syria's neighbor into the civil war, which has claimed at least 100,000 lives.

The operation to remove Homs from rebel control comes after the regime, backed by thousands of Hezbollah Islamist fighters from Lebanon, seized the neighboring town of Qusayr in a bloody bout of urban warfare. It produced numerous casualties on both sides before the regime established control and the rebels withdrew.

Hezbollah hasn't been as involved in the fighting in Homs, returning to limiting its assistance to military specialists, including communication technicians, snipers and elite special forces troops, according to a commander for the Shiite militant group whose unit fought in Qusayr.

"Hezbollah is not in Homs like we were in Qusayr," he told McClatchy. "Because Qusayr is along the Lebanese border and has many Shiite villages nearby, we took this as a mission that we could do. But the Syrian army doesn't need Hezbollah to fight in large numbers on the ground in most battles."

Elsewhere on Monday, the main Syrian exile opposition group suffered new turbulence at the top, when the prime minister of its still-notional interim government resigned, a spokeswoman said.

The resignation came two days after the group elected a new president as it tries to unify and arm the rebels fighting the Assad government and to help civilians in rebel-held areas of Syria.

The prime minister, Ghassan Hitto, was appointed in March to assemble an administration that would govern rebel-held territory. It was not immediately clear why he resigned.

But the opposition's efforts to establish that administration and a unified military command remain nascent at best. The United States and its allies have pledged to increase aid, but so far there has been little apparent impact, and members of the coalition have complained that it is hard to make progress when the West is not fully committed to helping them.

Hitto had taken a hard line against holding any talks with the Assad government, a stance that posed difficulties as the United States and Russia tried to organize peace talks in Geneva.

The New York Times contributed to this report.