BEIRUT — Syria’s prime minister, Mohammed Ghazi Jalali, said early Sunday that the government is ready to “extend its hand” to the opposition and hand over its functions to a transitional government.

“I am in my house and I have not left, and this is because of my belonging to this country,” Mr. Jalili said in a video statement. He said he would go to his office to continue work in the morning and called on Syrian citizens not to deface public property.

He did not address the claim by a Syrian opposition war monitor that President Bashar Al-Assad had left the country for an undisclosed location, fleeing ahead of insurgents who said they had entered Damascus after a stunning advance across the country.

The events suggested that the end of Mr. Al-Assad’s regime could be imminent after his bloody 14-year struggle to hold onto control as his country fragmented.

Rami Abdurrahman of the Syrian Observatory for Human Rights told the Associated Press that Mr. Al-Assad took a flight Sunday from Damascus.

State television in Iran, Mr. Al-Assad’s main backer in the years of war in Syria, reported that Assad had left the capital. It cited Qatar’s Al Jazeera news network for the information and did not elaborate.

An AP journalist at Damascus reported seeing groups of armed residents along the road in the outskirts of the capital and hearing sounds of gunshots.

The city’s main police headquarters appeared to be abandoned, its door left ajar with no officers outside. Another AP journalist shot footage of an abandoned army checkpoint where uniforms were discarded on the ground under a poster of Assad’s face.

Residents of the capital reported hearing gunfire and explosions. Footage broadcast on opposition-linked media showed a tank in one of the capital’s central squares while a small group of people gathered in celebration. Calls of “God is great” rang out from mosques.

It was the first time opposition forces had reached Damascus since 2018, when Syrian troops recaptured areas on the outskirts of the capital following a yearslong siege.

The pro-government Sham FM radio reported that the Damascus airport had been evacuated and all flights halted.

The insurgents also announced they had entered the notorious Saydnaya military prison north of the capital and “liberated” their prisoners there.

The night before, opposition forces took the central city of Homs, Syria’s third largest, as government forces abandoned it.

The city stands at an important intersection between Damascus, the capital, and Syria’s coastal provinces of Latakia and Tartus — Mr. Al-Assad’s base of support and home to a Russian strategic naval base.

The rebels’ moves into Damascus came after the Syrian army withdrew from much of southern part of the country, leaving more areas, including several provincial capitals, under the control of opposition fighters.

The fall of Damascus would leave government forces in control of only two of 14 provincial capitals: Latakia and Tartus.

The advances in the past week were by far the largest in recent years by opposition factions, led by a group that has its origins in Al Qaeda and is considered a terrorist organization by America and the United Nations.

In their push to overthrow Mr. Al-Assad’s government, the insurgents, led by the Hayat Tahrir al-Sham group, or HTS, have met little resistance from the Syrian army.

The rapid rebel gains, coupled with the lack of support from Mr. Al-Assad’s erstwhile allies, posed what could prove to be an insurmountable threat to his rule.

The UN’s special envoy for Syria, Geir Pedersen, called Saturday for urgent talks in Geneva to ensure an “orderly political transition.”

Speaking to reporters at the annual Doha Forum in Qatar, he said the situation in Syria was changing by the minute.

Russia’s foreign minister, Sergey Lavrov, whose country is Mr. Al-Assad’s chief international backer, said he feels “sorry for the Syrian people.”

President-elect Trump on Saturday posted on social media that America should avoid engaging militarily in Syria.

Separately, President Biden’s national security adviser said that the administration had no intention of intervening in Syria.