Though the BJP MLAs on Friday adopted a resolution on contesting the election and submitted its copy to Rangasamy seeking the support of its allies, the latter is yet to respond.
NDA allies AINRC and BJP seem to be engaged in a cat and mouse game, with both waiting for the other side to make the first move for discussions.
The counting of votes will be conducted on October 4 after the polling from 9 am to 4 pm.
Rajavelu earlier served as Welfare minister in the previous AINRC government in 2011-2016.
Three days after their swearing-in, five ministers of the AINRC-BJP government are yet to receive their portfolios.
The 32-year-old AINRC MLA representing Nedungadu constituency is the first woman Minister from Karaikal and the second in the Union Territory of Puducherry.
MLAs of AINRC, BJP, independent MLAs as well as opposition Congress MLA Ramesh Parambath from Mahe were present on the occasion.
BJP MLAs A Namssivayam and J Sai Saravana Kumar and AINRC MLA K Lakshminarayanan are in the list, sources said.
Puducherry Chief Minister N Rangasamy has completed a month in office, but the rest of the ministers are yet to be inducted.
Speaker to be from BJP, and his deputy from AINRC; all is well with NDA, says Saminathan
Known to be a simple, soft-spoken and accessible leader, Rangasamy is famous for driving around in a two- wheeler across the streets of Puducherry, even as a CM.
AINRC was heading the government in Puducherry in 2011.
N Rangasamy on Monday said the nearly five-year rule of the Congress in Puducherry in alliance with the DMK was a failure.