The bloc's foreign policy chief, Catherine Ashton, said ministers agreed to impose an asset freeze and visa ban on two companies and three people thought to be providing funding to President Bashar Assad's regime, CNN reported.
"The continuing violence is appalling," Ashton said.
There were reports of violence in Rastan, Deir Ezzor and other areas.
Initial reports indicated regime forces sustained heavy casualties during clashes at Rastan Monday, opposition activists said.
The Syrian Observatory for Human Rights said it received "preliminary information that three armored personnel carriers were destroyed and at least 23 soldiers were killed."
At least four people were killed Monday, including a child struck by gunfire from government forces in Deir Ezzor, said the Local Coordination Committees of Syria, an opposition network.
The organization said it received reports of troops aiming mortars and heavy artillery at al-Burnhanieh.
In bordering Lebanon, at least one person was killed and 45 wounded in fighting between pro- and anti-Assad factions, Lebanon's National News Agency reported.
U.N. monitors are observing progress of the suposed cease-fire in Syria and encouraging implementation of a peace plan brokered last month by U.N.-African League special envoy Kofi Annan.
On Saturday, the U.N. mission leader, Maj. Gen. Robert Mood, said 157 civilian and military monitors were in Daraa, Idleb, Hama and Homs provinces, the state-run Syrian Arab News Agency reported. About 300 observers are expected within weeks.
The LLC said more than 1,000 people have died since the cease-fire went into effect April 12.
The United Nations estimates that at least 9,000 people have died since the crisis began in March 2011.Opposition groups put the death toll at more than 11,000.
Syrian state-run media announced that results from last week's parliamentary elections will be announced Tuesday. More than 7,000 candidates vied for 250 parliamentary seats.