Replying to a calling attention motion in the House, he said the government was viewing the matter with utmost seriousness and would inform the state's concern over the issue to the prime minister in the next meeting with him.
Father Uzhunnalil hails from Ramapuram in Kottayam district of the state.
"As per reports, the plight of Fr Tom, who was abducted by IS terrorists on March 4, 2016, is serious. We have already sent letters and memorandum to the Centre seeking intervention for his release," Vijayan said.
Though it had been confirmed that the priest is in the captivity of terrorists, there is no information about where he is being kept, Vijayan said.
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The state has limitations in directly intervening in an issue in strife-torn Yemen, he said.
Moving the motion, Kerala Congress (M) chief K M Mani alleged that the centre was not showing any interest to speed up efforts for the priest's release.
If necessary, the centre should seek the help of the United Nations for his rescue from Yemen, he said.