The first occurred outside a state-run development agency in Ziyara, a village in the central province of Hama.
State media reported that two people had been killed and 10 others injured, but one activist group said at least 50 soldiers and militiamen had died.
The second blast left 11 people dead in Mezzeh 86, a predominantly pro-government district in the west of the capital, Damascus, officials said.
The violence came as the main opposition coalition, the Syrian National Council (SNC), announced that it had broadened its membership to more than 400, taking in activists and groups from inside Syria.
The move, announced at a meeting in Qatar, seeks to deflect criticism that the exile-led coalition fails to represent people on the ground.
On Thursday, SNC members will consider a US-backed proposal to set up a new 50-member leadership group that speaks for all the major opposition factions and includes military commanders and local councils.
The SNC would have a minority stake in the new leadership group, but some opposition figures are still sceptical that the effort will succeed.