The people of Kashmir have always viewed the pilgrimage as part of its "syncretic heritage", the parties said and pitched for ensuring peace and communal harmony in the state.
"The CPI(M) politburo denounces the dastardly attack on Amarnath pilgrims in Anantnag district in Jammu and Kashmir," the party said in a statement.
The CPI(M) said the attack signified the rise of religious extremism within the ranks of the militants and was intended at creating communal divide.
CPI national secretary D Raja asked the government to ensure the culprits of the "heinous and inhuman" attack do not go scot-free.
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"As the yatra is held every year, the government should strengthen intelligence and security measures," he added.
Seven Amarnath pilgrims were killed and 19 others were injured in the terrorist attack in south Kashmir's Anantnag district last night.
The bus, bearing Gujarat registration number, was on way from Baltal to Jammu when the attack took place.