Mr Chennithala made the plea in a letter to the prime minister.
Mr Uzhunnalil, who hails from Kerala, was abducted by terrorist group Islamic State which attacked an old-age home run by Mother Teresa's Missionaries of Charity in southern Yemeni city of Aden. At least 15 people were killed in the attack.
Video clippings of Mr Uzhunnalil was circulated on the social media today showing the bearded priest blindfolded, and being thrashed.
"It is unfortunate that the central government has been unable to secure his release," Mr Chennithala said in the letter.
He also wanted the Centre to treat the matter as "very serious" as the people of the state were anxious about the fate of the priest.
Kerala lawmakers raised the issue in the Parliament today and the government assured them that efforts were being made to secure his release.
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