France and the UK argue that the move would push Damascus towards a political solution.
However, several EU states are totally opposed to ending the arms embargo, which expires on 31 May.
Meanwhile French Foreign Minister Laurent Fabius said there
were "growing suspicions" of "localised" chemical weapons use in Syria.
Mr Fabius said the evidence needed "very detailed verification".
"We are consulting with our partners to examine what specific consequences to draw," he added.
He was speaking after the
French newspaper Le Monde on Monday reported that rebel forces in the Damascus suburb of Jobar had been targeted by canisters of toxic gas since last month.
In a conflict which worsens by the week, this is a week when critical decisions on the next steps in Syria must be made.
The US Secretary of State, John Kerry, has added his voice to
those urging Europe to ease restrictions on military support for the
opposition. "Fine for him to say, but what is Washington willing to do?"
one European foreign minister opposed to lifting the ban told me.
On Monday, Mr Kerry meets his Russian counterpart, Sergei
Lavrov, in Paris. Their talks are expected to focus on plans for the
first conference to bring together representatives of the Syrian
government and opposition.
The meetings in Brussels and Paris are linked. One of the main concerns in many European capitals is the
impact any lifting or easing of the EU arms embargo might have on the
fragile effort to fashion a political transition.
A photographer working for the paper "suffered blurred vision and respiratory difficulties for four days", it said.
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.
The meeting in Brussels comes as the US, France and Russia
push for Syria's opposition to join President Bashar al-Assad's
government at an international peace conference in Geneva next month.
Syria's foreign minister confirmed on Sunday that the government would "in principle" attend the summit.
Members of the main opposition coalition are currently
meeting in the Turkish city of Istanbul to decide whether to attend the
conference.
They have been given an unofficial deadline of this evening,
the BBC's Jim Muir reports, before US Secretary of State John Kerry is
due to have talks in Paris with Russian Foreign Minister Sergei Lavrov.
UK Foreign Secretary William Hague said that Britain fully
backed the Geneva conference as "in the end there is only a political
and diplomatically supported solution".
But he said amending the EU arms embargo was "part of
supporting the diplomatic work". President Assad's government needed "a
clear signal that it has to negotiate seriously", he said.
'Peace community'
Hours into the EU meeting, foreign ministers were still locked
in discussions on the arms embargo, says the BBC's Matthew Price in
Brussels.
A source told the BBC that a majority of countries preferred
not to change the embargo, and the ministers were seeking a compromise.
UK Foreign Secretary William Hague explained the government's position
One option could involve allowing some military equipment to be
sent to Syria, with strict conditions attached, our correspondent adds.
There are fears that anti-aircraft and anti-tank weapons
given to rebel fighters considered "moderate" might end up in the hands
of jihadist militants, including those from the al-Nusra Front, which
has pledged allegiance to al-Qaeda.
But last week Mr Hague told British MPs that weapons would be
supplied only "under carefully controlled circumstances" and with clear
commitments from the opposition.
Syrian state TV said Yara Abbas was killed while covering clashes in Qusair
