Suicide bombers detonated their explosives-laden vehicles near the facility in the countryside near Palmyra, the pro-government Ajel News website reported.
At least 30 people were injured, officials said.
In Damascus, meanwhile, activists reported fighting in Jobar, a suburb south of the Syrian capital, between the army and armed rebels, China's state-run news agency Xinhua said.
Activists said shells could be heard across the capital since early Wednesday amid reports the government forces were boosting their presence near Jobar to try to storm it.
The rebel Free Syrian Army has said it would "liberate" Damascus while Syria's official media said the capital is stable and denied reports security was deteriorating.
Fighting also was reported in and around Zamalka in southern Syria, Xinhua said.
The pro-government al-Watan newspaper said Syrian troops dealt "painful blows" to armed rebels Tuesday in Damascus and its southern suburbs, and in Homs and Hama.
The United Nations estimates more than 60,000 people, mostly civilians, have been killed since the uprising against President Bashar Assad began in March 2011.