Launching the campaign in Mudaliarpet, Bedi walked through the streets urging people to remove garbage and keep the environment clean.
A release from Raj Nivas said the former IPS officer appealed to residents to ensure that there was no room for mosquitoes to breed.
She was accompanied by District Collector E Vallavan and other officials.
On the other hand, Narayanasamy launched the campaign in Nellithope to educate the people on the need to eradicate mosquitoes and protect themselves from the vector-borne disease.
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The chief minister appealed to the people to keep their homes and environment clean.
Narayanasamy was elected from the Nellithope assembly constituency in the bypoll last year.
Bedi had recently expressed concern over increase in dengue cases in the Union Territory.
Narayanasamy had, however, said the dengue menace was under control and that anti-mosquito drive had been intensified at all levels and adequate supply of drugs and equipment were available.