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," Mr Palaniswami said.
As part of the government's resolve to address the issue, a storm water drain system is being constructed for the city's needs and the work is over on 300 km of the proposed 386 km long system, he said.
The entire work will be completed soon, he said without divulging further details.
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.
The chief minister said following the plans devised post-December 2015 deluge in the city, the government has ensured there was no stagnation of water this year despite the heavy downpour, he said.
"You saw how much of water stagnation was there in Bengaluru and Mumbai," Mr Palaniswami said while asserting that his government was doing a better job.
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.
Meanwhile, Principal Revenue Secretary K Satyagopal said a 43 personnel-strong team of State Disaster Response Force (SDRF) was camping in suburban Tambaram to attend to any kind of exigencies.