BEIRUT, Lebanon -- In another day of fierce fighting in the strategic Syrian town of Qusayr, government forces backed by fighters from the militant Lebanese group Hezbollah continued their offensive on Tuesday against anti-government rebels who have long held the town. There were conflicting reports about the progress of the fighting.
Warplanes mounted airstrikes on the town Tuesday morning, and government forces fired mortar shells as clashes intensified on the outskirts of the city, according to opposition activists. The Local Coordinating Committees, a network of activists tracking the fighting, said that at least 18 rebel fighters and civilians were killed.
Official Syrian and Hezbollah news outlets said the government offensive was making rapid headway in retaking Qusayr, a strategically situated town in Homs province, near the Lebanese border. The Syrian state news agency, SANA, said government troops had expanded their control from the eastern part of town into the center and north, destroying tunnels, weapons and explosive devicesy. The agency said a commander of Al Nusra Front, the extremist rebel group that the United States says is a terrorist organization, was killed in the fighting.
But the rebels said they were holding their ground in the town against the better-armed onslaught, had destroyed several armored vehicles and inflicted heavy casualties on the army, and would fight on in Qusayr. "The men are still standing strong on all fronts," said Ammar, an activist in Qusayr reached through Skype. "Their morale is very high and, God willing, military reinforcements from the Free Army should arrive soon."
Ammar was dismissive of the Syrian government's claims that its troops were gaining ground. "Yes, they've been holding large swaths of Homs for a while now," he said. "They are in control there, but they haven't made any real advances in Qusayr."
Ammar added that the rebels learned through an informant on Monday that Hezbollah fighters had decided to shift their tactics. Instead of trying to fight like conventional troops alongside the army, he said, the Hezbollah fighters now plan to infiltrate in small groups through back alleys at the edge of town and wage the guerrilla warfare for which they have been trained.
"But Hezbollah is still backed by the regime's warplanes," Amman said. "Now we have to wait and see who holds out for a longer period of time."
The combat of the last three days, including nearly continuous artillery shelling from the army, has claimed scores of civilian lives, he said, estimating the overall toll at 64 civilians killed and more than 500 wounded. "We have no way of rescuing them right now," he said. That estimate and others reports about casualties on either side could not be independently verified.
The fierce fighting in Qusayr pits mainly Alawite and Shiite fighters on the side of President Bashar al-Assad against rebels who are mostly Sunnis, further sharpening the sectarian schisms that have plagued Syria since a peaceful uprising turned into an armed rebellion. And there were reports of violence spilling over Syria's western and southern borders.
The Lebanese port city of Tripoli has been suffering some of the hottest clashes between Alawite and Sunni militants that have been seen there in months, Lebanese news outlets reported. Four people were killed there on Tuesday, after two civilians and two soldiers were killed on Monday, the reports said.
Syrian rebels near Qusayr and Hezbollah fighters just across the border in the Bekaa Valley of Lebanon have also traded artillery fire in recent days, accusing each other of endangering civilians with the imprecise weapons.
And SANA said on Tuesday that the Syrian army had destroyed an Israeli military vehicle that entered Syrian territory near the Golan Heights. Quoting the army's general command, the agency said the vehicle had crossed the Golan cease-fire line near the village of Bir Ajam and that Israelis had fired two rockets into Syria, causing no casualties.
SANA said that the alleged incursion was meant to raise the "collapsed morale" of rebels after blows they suffered in Qusayr. It was the second time in two days that Syrian state media, aiming to bolster its case that Syria's opposition is allied with Israel, claimed it had evidence of Israel aiding the rebels. On Monday, state media showed pictures of what it said was an Israeli jeep found in Qusayr but it appeared to be an old vehicle that experts said could have been supplied to Israeli-allied militias in south Lebanon years ago.
Capt. Eytan Buchman, a spokesman for the Israeli military, denied the Syrian version, saying, "This is taking things way out of proportion."
Captain Buchman said an Israeli military Jeep on routine patrol in the central Golan Heights had been hit from the Syrian side overnight, and had responded. "There was an Israeli jeep in Israeli territory," he said. "Syrians opened fire, we returned fire. The jeep was lightly damaged and we confirmed a direct hit on the Syrian target."
The Israeli military has struck Syrian targets near the cease-fire line about half a dozen times in recent months, after incidents in which it asserted that Syrian forces had intentionally targeted Israel. It has also counted more than two dozen incidents of stray rounds from internal Syrian battles landing in the Israeli-controlled Golan. Captain Buchman noted that there had also been reports in Syria on Monday about an Israeli vehicle being hit and said they were untrue.
The chief of the Israeli Defense Forces general staff, Lt. Gen. Benny Gantz, said at the University of Haifa on Tuesday that Israel "will not allow the area of the Golan Heights to become convenient grounds for Assad to operate on." Saying that Israel had "had enough," General Gantz added, according to local news outlets: "I am not a belligerent man, but we have to be prepared to defend ourselves. All in all, the situation in the Golan Heights is increasingly unstable."
As Hezbollah's role in supporting government forces in Syria has become more pronounced, the admiration that many Syrians once felt for the militant group has turned to disillusionment.
"I wasn't expecting that from them," said Qassem Tilawi, a commander in the Free Syrian Army who is fighting to unseat Mr. Assad.
Diana Rifai, a 23-year-old woman living in Beirut who volunteers at a camp for Syrian refugees in Lebanon, said around 100 Syrian families from Qusayr had sought refuge in the northern Lebanese area of Wadi Khaled during the past three days, many of them with injuries. She called the situation "devastating," saying that while some refugees were being taken in by Lebanese families, others were staying "in unfinished buildings or in storage rooms."
Ms. Rifai said that among the refugees, she had encountered a 4-year-old boy named Bashar who said he was ashamed to have the same given name as President Assad and had decided to call himself Mohammed instead.
Hania Mourtada and Hwaida Saad contributed reporting from Beirut, Lebanon, Hala Droubi from Dubai, and Jodi Rudoren from Jerusalem.
This article originally appeared in The New York Times.