Vijayan said Murugan's relatives met him this morning at the Assembly complex.
"We join the family in their sorrow. The government will ensure that such tragic experiences do not happen to anyone," the Chief Minister said in a Facebook post.
Vijayan said that the government would intervene to ensure that intensive care is provided to the patients when mishaps occur.
He had earlier apologised to the family of the migrant worker.
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The Chief Minister had promised all possible support to the family, she said.
In a memorandum submitted to Vijayan, she said her husband, who was working as a milkman at Kottiyam in Kollam district, was the family's sole bread-winner.
With his death, there was no one to look after her and her two minor sons, aged six and four and studyng in studying in standard 2 and LGK, she said.
"We have no permanent source of income to meet our daily needs and have no means to continue the education of my children other than that of seeking support of others," she said, adding they were very much in need of the government's support to continue their life further.