Hamdan airport in Deir Ezzor province on the border with Iraq, said activists monitoring the conflict.
In Paris, French President Francois Hollande met the National Coalition leader Ahmed Moaz al-Khatib on Saturday and afterwards told reporters he planned to let the group appoint an ambassador to France.
The post is to be filled by Monzer Makhous, an academic, although it was unclear if this would happen before a transitional Syrian government was formed.
Khatib, for his part, repeated his coalition's promise to build a transitional government composed of technocrats rather than politicians, and said it would include representatives of all ethnic and religious groups in Syria.
"There is no problem. The coalition exists and we will launch a call for candidates to form a government of technocrats that will work until the regime falls," Khatib told reporters.
But he appeared to have made little progress on his call for the West to arm the insurgency, which has led to an estimated 39,000 deaths since it began 20 months ago.
"The (rebel) Syrians need military means but the international community also has to exercise control," Hollande said.
He acknowledged that France could not act without agreement from its European Union partners: the EU has a strict embargo on arms deliveries to Syria.
"The protection of liberated zones can only be done in the framework of the international community," Hollande said after meeting Khatib.
"Once an alternative government has been formed, it can itself legitimately call for protection and support."
EU foreign ministers are due to discuss the embargo at talks in Brussels on Monday.
Hollande also said that Khatib, a Sunni imam, had assured him that the future government would include Christians and Alawites, the minority group to which President Bashar al-Assad belongs.
France, already one of Assad's harshest critics, on Tuesday became the first Western power to recognise the the opposition coalition as the sole representative of the Syrian people.
The new, broader-based opposition alliance was formed last weekend in Doha.
France, Turkey and the Gulf states have so far granted official recognition to the new Syrian grouping: Britain's foreign minister William Hague, who met Khatib on Friday, said London was considering following suit.
Israeli artillery fired into Syria early Sunday after gunfire from Syria hit an army vehicle but caused no injuries, the Israeli military said, in the latest spillover of violence from the bloody civil war raging across the ceasefire line.
"Shots were fired at IDF (Israeli army) soldiers...in the central Golan Heights," an army spokeswoman told AFP, adding that the Syrian fire hit "a vehicle."
"Soldiers responded with artillery fire towards the source of the shooting...a direct hit was identified," she said without elaborating.
It was the latest in several exchanges over the past week.
Last Sunday, Israeli troops fired a warning shot across the UN-monitored ceasefire line in response to Syrian fire, in the first instance of Israeli fire directed at the Syrian military in the Golan Heights since the 1973 war.
The following day, Israeli tanks fired again, confirming "direct hits" on the source of a mortar round that struck the Golan Heights.
On Thursday what the army described as "stray bullets" hit Israeli-controlled territory again.
Israel has complained repeatedly to the United Nations over the incidents and did so again after the latest shooting.
In eastern Syria, meanwhile, after battles lasting several weeks rebels seized Hamdan airport in the town of Albu Kamal in Deir Ezzor province on the border with Iraq, said the Syrian Observatory for Human Rights.
Syria's military had used the agricultural airport as a base for helicopter gunships.
Rebels also seized several tanks and mortars the army had stored there, said the Observatory, which relies on a network of activists, doctors and lawyers for its information.
"The rebels now control large swathes of land in the area," Observatory director Rami Abdel Rahman told AFP.
"The army has lost control of practically all the eastern border area, barring the Mayadeen military base" some 50 kilometres (30 miles) northwest of Albu Kamal, he said.
At least 66 people were killed across the country on Saturday -- 41 civilians, 24 rebels and one soldier -- according to the Observatory.
A Turkish journalist held by Syrian government forces since August was freed on Saturday and handed over to a group of Turkish opposition lawmakers after they met Assad, Turkish media reported.