The assault is the latest step in Mr Assad and Hizbollah's campaign to assert control over the Lebanese-Syrian border region and fortify the president's hold on central Syria, from the capital Damascus to his stronghold on the coast.
Syrian state media said the army had seized the nearby village of al Jarajeer, while rebels said Mr Assad's forces had advanced on the area but not completely taken it.
The military push came as international peace talks in Geneva stalled amid mutual recrimination, with the government resisting discussion of a post-Assad transition while the opposition called for a UN-monitored ceasefire.
There has been little let-up in fighting despite the start of the first peace negotiations three weeks ago after nearly three years of war. Mr Assad's forces seem to have had the better of recent fighting but outright victory seems out of reach.
US National Intelligence Director James Clapper told senators that prolonged stalemate seems likely, extending what he described as "an apocalyptic disaster" in Syria.
More than one-dozen air strikes hit the government's target area around Yabroud in the frontier mountains yesterday, the Syrian Observatory for Human Rights said.
A spokesman for rebel unit Liwa al Ghuraba said Hizbollah fighters and Assad forces were trying to position themselves on nearby hilltops to attack Yabroud.
Lebanese media said dozens wounded in Syria had been sent to Lebanese hospitals as well.
Concern about peace talks stalling prompted the international mediator in Geneva, Lakhdar Brahimi, to bring forward by a day to today a meeting with Russian and US officials in an apparent attempt to get Washington, which backs the rebels, and Mr Assad's ally Russia, to press their proteges for progress.
Continued strains between Russia and other world powers that have so far blocked United Nations action against the Syrian government showed little sign of easing. Russia said it would veto a UN resolution on aid, saying its wording seemed meant to open the way for foreign military action.
The Observatory said that, while the Syrian government and rebels have been at peace talks, Syrians have been killed at the fastest rate since the country slid into conflict in 2011,
At least 4959 people died in the three-week period between January 22, when the first round of Geneva 2 peace talks began, and February 11, the pro-opposition monitoring group said.
Rami Abdelrahman, the head of the London-based Observatory, said an average of 236 people had died each day in that period.
He added: "This is the highest average we have had. At other periods of time, we might have had a day with an extremely high toll, but the next day would be lower."
The Observatory estimated nearly one-third of those killed were civilians - and at least 515 of those were women and children killed in air raids and artillery strikes.
The three-year conflict has killed more than 130,000 people and forced around six million to flee their homes.