CPI National Secretary D Raja said that the law has taken its course.
Alleging that Congress and BJP were politicising the issue to gain mileage, he said "it is condemnable".
"This matter is not the concern of these two parties alone but of the entire nation," Raja said, adding the issue of timing has also led the people to raise several questions.
Former Himachal Chief Minister P K Dhumal said that the decision came late and only severe punishment can deter terrorists.
BJP workers took out a procession and distributed "laddoos" in Hamirpur in Himachal Pradesh.
BJP leader Yashwant Sinha congratulated President Pranab Mukherjee for rejecting the mercy petition of Afzal Guru.
Addressing a press conference in Hazaribagh, Sinha said the President deserved praise for rejecting the mercy plea.
"The President's action is a clear signal that terrorists have no place in the country," he said.