But there was no immediate decision to send arms to Syrian rebels and all other sanctions remained in force.
Even so, Russia said it would "directly harm" the prospects of an international peace conference on Syria.
Meanwhile, the BBC has heard evidence that 200 people were killed in a massacre in western Syria this month.
Opposition activists said they had documented the civilian deaths in al-Bayda and Baniyas after government troops and militias entered the towns.
The government described the operation as a strike against "terrorists".
The EU declaration on Syria came after 12 hours of talks in Brussels. Foreign ministers were unable to reach the unanimous decision required to extend the current arms embargo, and so agreed to renew the other sanctions - including an assets freeze on President Assad and his aides, and restrictions on trade in oil and financial transactions - without it.
The BBC's Jim Muir, in Beirut, says it is clear that the EU decision will not make much difference on the ground in the immediate future.
Member states can now decide their own policy on sending arms to Syria, but agreed not to "proceed at this stage with the delivery" of equipment.
The EU's Foreign Affairs Council is to review this position before 1 August, in light of fresh developments to end the conflict including the ongoing US-Russia peace initiative.
Britain and France had been pressing for the ability to send weapons to what they call moderate opponents of President Assad, saying it would push Damascus towards a political solution to the two-year conflict.
There has been increasing pressure on the international community to act since allegations emerged of chemical weapons being used in the conflict. Syria has denied using chemical weapons.
UK Foreign Secretary William Hague welcomed the outcome of the Brussels talks, saying it was "important for Europe to send a clear signal to the Assad regime that it has to negotiate seriously, and that all options remain on the table if it refuses to do so".
But other countries had opposed opening the way for weapons to be sent, saying it would only worsen the violence that has already cost at least 80,000 lives.
Austria had been a key opponent of arms being sent.
"The EU should hold the line. We are a peace movement and not a war movement," Austrian Foreign Minister Michael Spindelegger said.
Russian Deputy Foreign Minister Sergei Ryabkov called the EU move "a manifestation of double standards". Russia and the US are leading efforts to organise a peace conference on Syria next month.
The Syrian opposition has not said whether to attend the conference, and was locked in talks in Istanbul, Turkey, as an unofficial deadline to decide on its attendance passed.
A spokesman for the opposition Syrian National Coalition, Louay Safi, was quoted by news agency AFP as saying that the EU move was "a positive step", but that the coalition was "afraid it could be too little, too late".
George Jabboure Netto, a spokesman for the Syrian National Council, another opposition group, said the dropping of the arms embargo was a "step in the right direction".
He told the BBC that the SNC was willing to negotiate an end to the conflict, but only on the condition that there was no place for President Assad in the new Syria.
"We think coupling the arming of [the] Free Syrian Army with diplomatic efforts is a must for any hopes for the diplomatic efforts to succeed."
The EU embargo, first imposed in May 2011, applies to the rebels as much as the Syrian government.
But in February this year, foreign ministers agreed to enable any EU member state to provide non-lethal military equipment "for the protection of civilians" or for the opposition forces, "which the Union accepts as legitimate representatives of the Syrian people".
UK aid agency Oxfam has warned of "devastating consequences" if the embargo ends and more arms are sent into Syria.
In other developments:
French officials are testing samples brought back from Syria by two journalists for Le Monde newspaper, who say they witnessed a chemical weapons attack by government forces against the rebels on the outskirts of Damascus last month
US Secretary of State John Kerry met Russian Foreign Minister Sergey Lavrov in Paris, with Mr Kerry saying they were both "deeply committed" to a transitional government in Syria chosen by mutual consent
One of the strongest advocates of US military aid for the Syrian opposition, Senator John McCain, has made a surprise visit to Syria for discussions with rebel leaders
Fighting in Syria continues around the strategic town of Qusair, a few miles from the Lebanese border, with a prominent Syrian female TV journalist, Yara Abbas, killed just outside the town
Three Lebanese have been killed near the north-eastern town of Arsal by gunmen who then fled across the border into Syria, officials said.