In a letter to Singh, she said Indian embassy officials may be asked to render all necessary medical and other assistance to the three injured.
Reminding Singh of Centre's efforts to get compensation to the families of two fishermen killed by Italian cargo vessel Enrica Lexie off Kollam in Kerala in February this year, she said efforts should be made to ensure compensation was paid to the families of the deceased and injured fishermen.
'I request you to kindly take up this matter with the Governments of the United States and Dubai, to cause a detailed inquiry into the incident. I also request you to ensure that due compensation is paid to the families of the deceased and injured fishermen,' she said.
'As the dead and injured fishermen are innocent fishermen who were conducting fishing in the sea only for their livelihood, please ensure that justice is rendered,' she said.
The Chief Minister also announced a relief of Rs five lakh to the kin of the deceased Sekar and Rs 50,000 each to the three injured.
Meanwhile, DMK chief M Karunandhi, whose party is a key constituent of the ruling UPA, urged the Centre to 'strongly condemn' the incident.
'I urge the government to take steps to ensure compensation for the deceased and the injured from the US,' he said in a statement.
DMDK founder and Leader of the Opposition in Tamilnadu Assembly, Vijayakanth, also asked the Centre to ensure compensation for the victims.