(CNN) -- Two Syrian jets fired three rockets that hit empty buildings near the Lebanese town of Arsal near the Syrian border Monday, a local source said. There were no injuries, according to the source.
Also, Lebanese state-run news agency NNA reported that Syrian warplanes attacked sites in northern Lebanon.
The government's use of fighter jets to fire rockets into Lebanon is a "significant escalation," U.S. State Department spokeswoman Victoria Nuland said Monday.
The French Foreign Ministry in Lebanon issued a statement condemning the attacks.
"The aerial bombing carried out today by the armed forces of the Syrian regime on Lebanese territory, in the region of Ersal, is a new and serious violation of Lebanon's sovereignty," the statement said. "France strongly condemns this escalation and reiterates its commitment to Lebanon's sovereignty and the inviolability of its borders."
This latest violence comes as the Syrian conflict enters its third year. The unrest started in March 2011 when President Bashar al-Assad's government launched a fierce crackdown on protesters. The discontent evolved into a full-blown civil war that has left more than 70,000 dead and more than 1 million refugees.
One result of the warfare is the spillover of fighting and refugee displacement into neighboring countries such as Lebanon, Turkey, Jordan and Iraq.
As for Lebanon, the state-run Syrian Arab News Agency also reported border flareups.
Syrian armed forces and border guards have thwarted "armed terrorist" infiltrators attempting to get into the Homs countryside from Lebanon, SANA said, citing a development first reported last week.
The news outlet also reported gunshots fired at Syrian border checkpoints from Lebanon.
Syria's Foreign and Expatriates Ministry accused the alleged terrorists of receiving "clear logistic support from inside the Lebanese lands" and ferrying their wounded and dead in ambulances across the Lebanese border. SANA quotes a source saying that security forces have killed and wounded fighters and forced them to retreat to Lebanon.
Last Thursday, the U.N. Security Council voiced "grave concern over repeated incidents of cross-border fire which caused death and injury among the Lebanese population, incursions, abductions and arms trafficking across the Lebanese-Syrian border, as well as other border violations." The declaration followed a briefing by officials on how the conflict in Syria has spilled into Lebanon.
Other violence raged in Syria on Monday, with the opposition Local Coordination Committees of Syria recording at least 53 deaths.
Arming the opposition
The United States and Western allies have staunchly opposed the Assad government, but it has balked at arming Syria's rebels, who have been getting weapons from some Arab nations and seizing or buying them from Syrian soldiers.
As the carnage continues, however, the West is taking a different tone.
Secretary of State John Kerry said Monday that the United States would not hamper the arming of Syrian rebels by allies.
"President Obama has made it clear that the United States does not stand in the way of other countries that have made a decision to provide arms," he said.
His comments, made at the State Department, come as Britain and France urge the European Union to lift the weapons embargo in order to arm moderate Syrian rebels.
Kerry acknowledged the need to change the military "imbalance" on the ground in order to change al-Assad's "calculus."
"Right now, President Assad is receiving help from the Iranians, he's receiving help from al Qaeda-related, some elements, he's receiving help from Hezbollah, and obviously some help is coming in through the Russians. If he believes he can shoot it out, Syrians and the region have a problem and the world has a problem," he said.
Last week, Syrian rebels told CNN that the United States is helping organize training for Syrian rebels in Jordan in the use of anti-tank and anti-aircraft weapons.
Opposition selects leader
A Syrian opposition umbrella group, meeting in Istanbul, Turkey, has chosen a U.S.-educated Kurdish businessman to head its provisional government, an opposition activist who attended the vote said Monday.
Ghassan Hitto, an information technology executive who went to college in Indiana and lived for many years in Dallas was elected Monday to lead a government whose specific role may be spelled out at a planned news conference Tuesday.
Hitto was born in Damascus and is a member of the board of the Syrian American Council, the council said in a news release after the vote.
The group said the decision should assuage the Obama administration's concerns about who would lead Syria should President Bashar al-Assad be deposed.
"This question has now been answered," the council's statement said.
CNN's Nick Paton Walsh, Joe Sterling, Elise Labott, Jason Hanna, Raja Razek, Yousuf Basil and Jim Kavanagh contributed to this report.