The Wednesday incident prompted the opposition Syrian National Council to call for the U.N.
The Syrian National Council, consisting mainly of exiles, is failing to gain diplomatic traction.
The opposition umbrella group the Syrian National Council (SNC), meanwhile, said 250 had died over Monday and Tuesday.
The Syrian National Council recently published a letter thanking the citizens of Iran.
The Syrian National Council, a main political opposition group, said there will be "no dialogue and no partnership" with al-Assad's regime.
The Syrian National Council is a divided gaggle of exiles, with only limited authority in a place they still call home.
The Syrian National Council (SNC) said Hezbollah fighters attacked three villages near the Lebanese border in support of the Syrian government.
Officials from the Syrian National Council said the suspension indicated it was time for world leaders to take more severe steps.
If the Syrian National Council ultimately does take charge, it may struggle to contain the worst excesses of the militia groups, he said.
CNN: Syria: As al-Assad's grip loosens, what could come next?
The opposition Syrian National Council has called for an emergency UN Security Council meeting "so that it can issue a resolution to protect civilians".
Over the weekend, the opposition Syrian National Council elected minority Kurdish activist Abdul Basit Sieda to unite dissidents seeking to oust Syrian President Bashar al-Assad.
The Syrian National Council, the Syrian opposition, congratulated Pope Francis and called on him to pay special consideration to the suffering of the Syrian people.
The opposition Syrian National Council has accused the Syrian government of planning Monday's explosion, but has not offered any evidence to back up that claim.
The Syrian National Council (SNC), which was formerly recognised as the main opposition, had been concerned it might be sidelined by the new opposition body.
The country's main opposition coalition, the Syrian National Council (SNC) said the attacks had been carried out by Mr Assad's government to discredit its critics.
The Syrian National Council, a group mainly of exiles, includes several.
Dozens of countries have recognized the Syrian National Council as a legitimate representative of the Syrian opposition, though many members of the group's leadership are expatriates.
"Our Foreign Minister rejected meeting with the Syrian National Council until they widened their base to include different religions and sects, " a Foreign Ministry spokesman said.
In what may be a blow to the regime, the opposition Syrian National Council said Wednesday that two senior Syrian diplomats were the latest to defect.
Russia has recently been pivoting in an anti-Assad direction, saying that it would suspend arms sales and holding talks with the Syrian National Council.
Political opposition groups, including the Syrian National Council, and fighters such as the Free Syrian Army, have emerged and become key players in the opposition movement.
The plan's vague wording gives the regime wiggle room and has created difficulties for the Syrian National Council, which views his resignation as a condition for talks.
"We consider the defection to be what is morally right and what is called for at this historic time, " said Abdulbaset Sieda, head of the Syrian National Council.
Adib al Shishakly, a member of the Syrian National Council, an umbrella group of exiles, said Damascus needs to abide by all six points of Annan's peace plan.
"We cannot overlook the fact that Kofi Annan's proposals have not been agreed to by some of the opposition groups, including the well-known Syrian National Council, " Lavrov said.
Burhan Ghalioun, the professorial leader of the Syrian National Council, the main opposition group in exile, has pledged to oversee and organise the rebels, but not to equip them.
Speaking on Al Arabiya TV, the former head of the Syrian National Council, which preceded the coalition, said that he and other coalition members were surprised by the resignation.
The Syrian National Council, an opposition coalition that includes many exiles, is set to make a presentation at the Istanbul meeting to summarize its efforts to unite the opposition.
Consequently, Turkey rapidly emerged as one of the boldest supporters of the Syrian opposition, and the Syrian National Council, formed as the dissidents' umbrella group, found a base in Turkey.
Burhan Ghalioun, of the Syrian National Council - the divided body which says it represents the political opposition to Mr Assad - said Russia was standing in the way of progress.
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