Chief Minister Vijayan wrote to Union External Affairs Minister (EAM) S. Jaishankar urging him to ensure that adequate relief measures are taken.
"It is reported that several Indians including Keralaites have lost their lives. We request that you take adequate steps to bring relief to the affected," he said in the letter.
Leader of the Opposition V.D.Satheesan urged the state government and the Centre to ensure that there is proper coordination in relief and rescue operations.
The fire broke out in a six-floor building crammed with migrant workers in al-Mangaf area of Kuwait City.
The blaze occurred while the workers were asleep and some residents had to jump from the building in an attempt to survive, Kuwaiti newspaper al-Qabas reported, citing witnesses.
Local media reported that 49 people have died in the fire tragedy.