Addressing party workers at the Puthrikandam maidan here on the conclusion of the party's 15-day 'Jan Raksha' Yatra in the state, Shah alleged that the 13 workers were killed after the present government came to power in May last year.
"I am asking the Kerala chief minister, whether he is prepared to take moral responsiblity for the killing of 13 BJP/RSS workers in the state after the LDF government came to power."
Shah said if the Marxist party feels that BJP/RSS workers can be eliminated through violence even after 70 years of independence, "they are mistaken."
"I will like to tell CPI(M) that it is not possible," the BJP chief said.
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He also asked Vijayan whether people had given him the mandate for elimination of BJP/RSS workers in the state.
Earlier, Shah walked with party workers for about two km from the Martyr's column at Palayam to Putharikandam maidan, near the famous Padmanabhaswamy temple.
He also paid tributes to party workers who had lost their lives in political violence in the state before addressing the public meeting.
Shah had flagged-off the yatra at Payyannur in Kannur, the northern district of the state with a history of clashes between CPI(M) and BJP-RSS workers, on October 3.
The padayatra was to highlight the 'Left's atrocities' in Kerala under the LDF government.
Earlier, Rajesekharan denied allegations by the ruling CPI(M) and opposition congress that the march was to create communal divisions in the society.
Union minister Pon Radhakrishnan said the yatra was to save' the people of the state.
The padayatra had criss-crossed 11 districts in the state with four chief ministers, including Yogi Aditiyanath of Uttar Pradesh, senior party leaders and Union ministers taking part in the high-pitched campaign against the ruling LDF.
Remarks by BJP leaders also kicked up controversies as the march progressed.
Adityanath wanted Kerala to learn from UP's record in health care and Goa chief minister Manohar Parikkar alleged that Kerala was being ruled by 'rogues', triggering counter remarks from the CPI-M.
Shah had walked about seven km from Payyannur to Pilathara in the district during the rally.
Representatives of the NDA partners in the state-- Tushar Vellapally of BDJS (Bharat Dharma Jana Sena), Tribal leader C K Janu of Janadhipathya Rashtriya Sabha, P C Thomas of Kerala Congress (Thomas) were among those who attended the public meeting.