Accompanied by his deputy O Panneerslevam and senior officials, the chief minister visited RK Nagar and Perungalathur on the city outskirts.
"Low-lying areas with water-logging were identified in the Chennai Corporation (limits) and Kancheepuram district. Workers (here) worked on a war-footing and stagnant water has been removed," he told reporters.
People asked me to devise a permanent solution to the issue of inundation, Palaniswami said.
The entire work will be completed soon, he said without divulging further details.
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Chennai received 36 cm of rains in the last three days, the AIADMK leader said, adding, the government acted "quickly" to ensure there was no water stagnation in the city.
To a question, he said encroachments on water bodies were being removed in line with court orders, and denied that there was any delay in this work.
"You saw how much of water stagnation was there in Bengaluru and Mumbai," Palaniswami said while asserting that his government was doing a better job.
Tamil Nadu ministers accompanied by designated officials have fanned out to various affected areas and are overseeing the relief activity, he said.
The state government has been facing criticism from the opposition, including DMK, over handling of the monsoon fury.
They have also questioned the claim of the state government that it had undertaken desilting works ahead of the monsoon.