In a Facebook post, Lakshadweep Administrator Farooq Khan said "with the grace of God", there had been no loss of human life, but property damage in some islands was very high.
He said the public of all islands exhibited exemplary courage in rescuing more than 250 fisherman from Tamil Nadu, Karnataka and Kerala.
Thanking all islanders on behalf of the Centre and his administration for their 'selfless work' during the troubled times,Khan said the authorities had immediately started relief and rehabilitation work and details were being speedily collected from authorities concerned.
Four ships were sent by the Navy with relief materials and for carrying out relief and rescue operations.
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"Let us all thank God almighty for saving our lives and let us also cooperate with each other to complete the relief and rehabilitation process expeditiously," Khan said.
Meanwhile, many islanders, who had come to the mainland for various purposes,including treatment,are stranded in Kochi and Kozhikode as ship and flight services have been cancelled.
Sources said many of them were struggling as they have run out of money.
Lakshadweep MP P P Mohammed Faizal yesterday said precautionary measures taken by the administration soon after receiving the cyclone alert helped save lives in the island.
He said Lakshadweep islands suffered a loss of over Rs 500 crore.
Normal life in three islands -- Minicoy, Kalpeni and Kavaratti -- was badly hit by the cyclone.
Around 500 houses were damaged, several coconut trees uprooted and electric and communication lines were disrupted due to the calamity in Minicoy island alone, he said.