British Minister for the Middle East Alistair Burt met in London with Abdul Hakeem Bashar, leader of the opposition Syrian Kurdish National Council.
Burt, in statements following the meeting, noted a united Syrian opposition was "crucial" for a transition to a free and democratic Syria.
"I reiterated the clear and growing need for the Syrian opposition to come together to help define a shared vision for a future Syria where the political system is inclusive, representative and adheres to international human rights standards," he said.
European foreign ministers scheduled a Monday meeting to consider another round of sanctions against Damascus. Measures at the U.N. Security Council remain stalled in part because of objections by veto-wielding Russia.
The British government, in a statement, said it has generated a "list of 21 military and security officials we believe are responsible for the violence against civilians."
A monitoring team with the Arab League is on the ground in Syria in an effort to ensure the regime is complying with a pledge to pull military forces from the streets. At least one member of the team resigned because of ongoing violence.
An opposition group this week told London's pan-Arab daily Asharq al-Awsat that the death toll has topped 6,000 since mid-March.
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