According to the LCC, the latest concentration of killings by security forces happened in the Jobar district of Homs. The group said 20 of the dead belonged to a single family, and 16 to another.
It said the deaths were reprisal killings, coming days after security forces retook Homs from rebels, having pounded the city for weeks.
The claims cannot be verified as international media inside Syria are heavily restricted.
After visiting Homs, one of the first cities to join the uprising last March, the UN humanitarian chief Baroness Valerie Amos said the bombed-out Baba Amr district felt like it had been closed down.
"The devastation there is significant, that part of Homs is completely destroyed and I am concerned to know what has happened to the people who live in that part of the city," Baroness Amos told Reuters news agency.
Activists said troops committed massacres after they went in to the district, but Damascus blamed the rebels for many deaths.
The BBC's Jim Muir in neighbouring Lebanon says activist groups continue to report the summary execution of men from Baba Amr, the butchering of entire families, and the systematic mass rape of women.
Our correspondent says opposition groups are urging Baroness Amos to go back and delve deeper.
The UN says more than 7,500 people have died as a result of the violence in Syria over the past 12 months.'
Switzerland condemns Syria for doing this and we hope for a swift and peaceful end to the violence and a peaceful and orderly transition of power.
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