At the same time the party maintained that the Centre should ensure that the dialogue process with Pakistan continues.
"The central committee expressed its deep concern at the raising of tensions on the Line of Control in Jammu & Kashmir. It strongly condemns the killing of two Indian soldiers and beheading of one of them. The Government of India should take a firm stand and convey to the Pakistan authorities that such attacks are unacceptable and cannot be tolerated," a press statement of CPI(M) central committee said.
"While maintaining a tough stance the Indian government should also ensure that the dialogue process with Pakistan continues and there should be no curbs on the people to people relations being developed between the two countries," the statement said.
The CPI(M) also harped on the issue of high level talks with Pakistan government to ensure that violations of the ceasefire do not recur.