* No international flights to Damascus - airline says
* Damascus resident reports black smoke to the south, east
* 12 Lebanese gunmen killed in Syria
* Clashes near airport road; Internet still down
BEIRUT, Nov 30 (Reuters) - Syrian air force jets bombarded rebel targets on Friday close to the Damascus airport road and a regional airline said foreign carriers had halted flights to the capital.
Activists said security forces clashed with rebels trying to topple President Bashar al-Assad around Aqraba and Babilla districts on the southeastern outskirts of Damascus which lead to the international airport.
Internet connections and most telephone lines were down for a second day, the worst communications outage in a 20-month-old uprising in which 40,000 people have been killed and hundreds of thousands forced to flee the country.
The mostly Sunni Muslim rebels who are battling Assad, from Syria's Alawite minority linked to Shi'ite Islam, have been making gains around Syria by overrunning military bases and have been ramping up attacks on Damascus, his seat of power.
A spokesman for a rebel Military Council in Damascus, Musaab Abu Qitada, told Reuters on Thursday they were also trying to "liberate" the airport to stop planes they said were delivering arms to the government.
A resident of central Damascus said he saw black smoke rising from the east and the south of the city on Friday morning and could hear the constant boom of shelling. State television said Assad's forces were fighting rebels in those areas.
U.N. Secretary-General Ban Ki-moon said the conflict had reached "new and appalling heights of brutality and violence".
The government had intensified its campaigns to root out opposition strongholds and increased shelling and air strikes, Ban told the U.N. General Assembly. "Opposition elements also have stepped up their attacks. I am horrified and saddened and condemn the seemingly daily massacres of civilians," he added.
An aviation source in neighbouring Jordan said two Syrian Air flights crossed Jordanian air space heading for the Syrian capital on Friday evening and that Damascus airport was open, although international airlines were staying away.
The head of the national airline Syria Air said its services were operating according to schedule, state television reported.
EgyptAir and Emirates have suspended flights to Damascus in response to the recent violence and there was no sign that Air Arabia and flydubai had flown scheduled trips on Friday.
"Airlines are not operating to Damascus today," said a Dubai-based airline official.
The Syrian Observatory for Human Rights, a British-based opposition monitoring group, said jets were bombarding targets in rural areas around Aqraba and Babilla.
The Observatory's director, Rami Abdelrahman, said the airport road was open, but there was minimal traffic.
"A DECISIVE PHASE"
U.S. and European officials said rebels were making gains in Syria, gradually eroding Assad's power, but said the fighting had not yet shifted completely in their favour.
A Damascus-based diplomat said he believed the escalation in fighting around the capital was part of a government offensive which aimed to seal off the state-controlled centre of the city from rebel-held rural areas to the south and east.
Activists say Assad's forces have also been shelling the Daraya district to the southwest of the city, trying to prevent rebels from cementing their hold of an area which could give them a presence in a continuous arc from the northeast to southwest of the capital's outer districts.
"I don't know whether the shelling has succeeded in pushing back the FSA (rebels) - experience shows that they return very quickly anyway," the diplomat said. "We seem to be entering a decisive phase of the Damascus offensive."
At least 12 Lebanese gunmen were killed in a Syrian army ambush in the central Syrian province of Homs, a security source said on Friday, highlighting how Lebanon's neighbours are being dragged into the war.
The sources said the Lebanese men were killed near the town of Tel Kalakh and were from majority Sunni northern areas of Lebanon.
WHO CUT THE INTERNET?
Syria's Internet shut down on Thursday, a move which activists blamed on authorities but which authorities variously attributed to a "terrorist" attack or a technical fault.
Global hacking network Anonymous accused Syria's government of blocking communications to silence critics and said it would respond by attacking Syrian government websites around the world.
"As we discovered in Egypt, where the dictator (Hosni) Mubarak did something similar - this is not damage that can be easily or quickly repaired," Anonymous said, referring to an Internet outage during the 2011 uprising in Egypt.
French foreign ministry spokesman Philippe Lalliot said the communications cut was of a matter of "extreme concern".
"It is another demonstration of what the Damascus regime is doing to hold its people hostage. We call on the Damascus regime to reestablish communications without delay," he said.
CloudFlare, a firm that helps accelerate Internet traffic, said on its blog saboteurs would have had to simultaneously cut three undersea cables into the Mediterranean city of Tartous and also an overland cable through Turkey in order to cut off the entire country's Internet access.
"That is unlikely to have happened," it said.