Syrian forces bombarded opposition strongholds in Damascus on Sunday and a car bomb exploded in the central Syrian city of Homs, as fierce fighting between government troops and rebels continued unabated.

The extraordinary assault on the outskirts of Damascus, the capital, was the most intense fighting in four months, as government troops tried to stall rebel forces from advancing further into the stronghold of President Bashar al-Assad.

Reports from state-run media said that at least 15 people were killed and more than 20 were injured, some critically, after a car bomb went off on al-Hamra Street in an upscale section of Homs filled with restaurants and cafes. Many Syrians fleeing fighting elsewhere in the city have settled in the area.

Video posted online showed flames and thick black smoke billowing from the street in front of an apartment building as onlookers screamed and others rushed toward the blaze carrying red fire extinguishers.

In Damascus, Syrian forces fired rockets into suburban neighborhoods where rebels have advanced in recent days. The operation appeared to be an effort to stop opposition fighters from closing in on the city center.

A look at the Syrian uprising nearly two years later. Thousands of Syrians have died and President Bashar al-Assad remains in power, despite numerous calls by the international community for him to step down.

Activists said clashes continued for a fourth day around Damascus’s international airport, but the government announced that the airport was open and that flights were operating on schedule. Egypt Air said it would resume flights Monday.

The day’s events suggested that the Syrian government is leaning more on its air force since rebels have overrun some army bases and seized heavy weaponry.

A group called the Aleppo Military Council announced that it is prepared to shoot down Syrian fighter jets. The group did not specify what it would use but said it is “very ready to accomplish these attacks,” implying that it has antiaircraft missiles.

The commander of a ­Damascus-based militia with about 15 members said its fighters had assassinated an air force officer last week and are prepared to kill more in an effort to drain the regime’s air power.

“We waited for him in the street and shot him,” said the commander, who used the nom de guerre Abu Omar al-Shami during an interview in Turkey, where he said he had come to raise money to buy silencers for the militia’s pistols.

There also was heavy fighting Sunday in the countryside around Idlib in northwestern Syria. Refugees who arrived in Turkey on Sunday said the Syrian army had intensified the shelling of numerous farming villages where residents have taken part in anti-government rallies.

On the Turkish side of the border late Sunday morning, the dull thud of explosions came every few minutes from the far side of a mountain across a large valley separating the two countries.

Salame Diab, a 28-year-old Syrian farmer, arrived midday in the Turkish border town of Hacipasa. He said at least half of his village of Ayn Assauda had been destroyed Saturday by almost nonstop government shelling. He took his wife and four children, and together with most of the villagers, left town on foot around 3 a.m. Sunday for the 10-mile trek to Turkey. Some villagers stayed behind, Diab said, to care for their sheep and cattle.

The Turkish humanitarian group Support to Life distributed food, blankets and clothing to the refugees, who are not counted as registered because they entered the country illegally. Program director Derya Mutlu said the new arrivals could sleep in an empty wedding hall owned by the village. Blankets and tables lined the walls of the room, beneath a worn roof riddled with holes.

Other refugees who were turned away at the border reached Turkey in a rowboat operating as a makeshift ferry, across a river slicing through an olive grove outside town.

“We got out before the traitorous Syrian army entered our village,” said a man who alighted from the tiny rowboat with his wife and seven children. The man, who declined to give his name, said that most of the homes in his village of Selet Zahour were reduced to rubble by artillery about two weeks ago and that the rest were burned by government troops.

NATO is expected on Monday to consider whether to provide Turkey with Patriot missiles that it has requested for placement along the Syrian border. Turkish officials fear that if the Syrian government is backed into a corner, it may deploy missiles with chemical warheads. The Patriot missiles would be used to deflect Syrian projectiles before they reach Turkish border communities.

Stray Syrian missiles and shells have occasionally landed in Turkish territory. Several rockets fell in fields around Reyhanli on Saturday night.

On Sunday morning, farmers and young boys climbed a hilltop near a school and a mosque where an errant missile left a crater about four feet deep in a rocky field. Some of the boys picked up sharp pieces of metal that were all that remained of the rocket after police carried it away.

Several people who live nearby described how their iron doors rattled and windows broke when the rocket landed around 8 p.m. Saturday.

“It’s like the house was shaken off its foundation,” said Leyla Parlar, who lives about 500 feet from the site, as she displayed a small plastic bag filled with pieces of the weapon she found outside and on her roof, patio and living room carpet.

In all, at least 85 people died in fighting and violence in Syria on Sunday, according to the Syrian Network for Human Rights.

That was down considerably from more than 200 counted as dead on Saturday by the Britain-based Syrian Observatory for Human Rights. The 20 months of civil war have claimed more than 40,000 lives.

Syrian state-run television showed gruesome photos of 21 Lebanese from Tripoli who were ambushed and killed as they crossed the border two days earlier. The television report called them “terrorists” and showed their ID cards. In Tripoli, their relatives held a protest march.

Ahmed Ramadan contributed to this report.