The United States is struggling to track a fragmented Syrian opposition and has found it increasingly difficult to get a clear picture of rebel factions, the U.S. military's top officer said Monday.

"About six months ago we had a very opaque understanding of the opposition and now I would say it's even more opaque," General Martin Dempsey, chairman of the Joint Chiefs of Staff, told the Center For Strategic and International Studies (CSIS), a Washington-based think tank.

U.S. State Department spokeswoman Victoria Nuland condemned on Monday the Syrian bombing of Lebanese border regions, stating that “this step violates the country's sovereignty and is absolutely unacceptable”.

“Syrian warplanes Monday bombed northern Lebanon for the first time,” Nuland confirmed to reporters, denouncing the move as "a significant escalation" of the conflict.

The United States will not oppose moves by some European nations to arm Syrian rebels battling President Bashar Assad, top U.S. diplomat John Kerry said Monday.

"President (Barack) 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, whether it's France or Britain or others," Kerry told reporters.

NATO head Anders Fogh Rasmussen insisted Monday that the military alliance had no intention of getting dragged into an EU debate about whether or not to supply arms to the Syrian rebels.

"This issue is a European Union question ... I have no intention whatsoever to interfere with this discussion within the EU," Rasmussen told a press conference.

The United Nations defended its humanitarian work in Syria on Monday, saying it deals with all parties in a "neutral and transparent manner" and offers assistance to all those affected by the conflict.

Radhouane Nouicer, the regional coordinator for the U.N.'S OCHA humanitarian affairs office, said the organisation was working under tough conditions and repeated a call for additional funding.

Progressive Socialist Party leader MP Walid Jumblat called on Monday for respecting the cabinet's policy of disassociation towards Syria's war, warning against the “trap the neighboring country's regime is planning for Lebanon”.

"Political and security dangers resulting from the weak execution of the policy of disassociation are threatening Lebanon's stability,” Jumblat stated in his weekly editorial to the PSP-affiliated al-Anbaa website. “We must avoid dragging Lebanon into Syria's turmoil”.

Syria's rebel chief said in Istanbul on Monday that the mainstream rebel Free Syrian Army wants an interim government to administer the whole of Syria and not just the areas freed from regime forces.

The demand came as the main opposition Syrian National Coalition met in Turkey to select an interim prime minister and government for large swathes of territory in the strife-torn country that have slipped out of President Bashar Assad's hands.

Syrian warplanes bombed the border area with Lebanon for the first time on Monday, a high-ranking Lebanese army official told Agence France Presse, reportedly targeting Syrian rebel positions inside Lebanon.

"Syrian planes bombed the border between Lebanon and Syria but I cannot yet say if they hit Lebanese territory or only Syrian territory," the military official said, speaking on condition of anonymity.

More than 6,800 women and children have been killed in two years of fighting in Syria, the Syrian Observatory for Human Rights watchdog said on Monday, putting the total toll at around 59,000 dead.

That figure is lower than the roughly 70,000 people that the United Nations says it believes have been killed since Syrian opposition activists began an uprising against the regime of President Bashar Assad.

Syrian regime forces resumed shelling parts of Damascus on Monday as security forces carried out arrests of students in housing attached to Damascus University, a monitoring group said.

"There is shelling of the areas of Maadaniya (south) and Jubar (east) by regime forces," the Syrian Observatory for Human Rights said, reporting sniper fire and casualties in the city's northern Barzeh district as well.