There are 30 Assembly constituencies spread over Puducherry, Karaikal, Mahe and Yanam regions.
Counting began amid tight security and in strict adherence to the Covid protocols.
A spokesman of the Election Department here told P T I that postal ballots were taken up first for counting.
This would be followed by counting of votes recorded in Electronic voting machines (EVMs) at 8.30 AM, the spokesman said.
There are three counting centres in Puducherry region -Motilal Nehru Government Polytechnic college, the Women`s polytechnic college and the Government Tagore Arts and Science college (all in neighbouring Lawspet)-relating to the 23 segments in Puducherry.
Counting of votes would take place simultaneously in Karaikal (having five constituencies) and Mahe and Yanam regions having one segment each.
Chief Electoral Officer Shurbir Singh told P T I that more than 17,300 postal ballots have been received in the whole of Union Territory.
The election authorities banned victory processions and also distribution of sweets in view of the necessity to curb congestion and also prevent possible spread of pandemic.
Nearly 82 per cent of the 10.04 lakh voters had exercised their franchise in the Union Territory on April 6.
As many as 324 candidates jumped into poll fray and they included party sponsored nominees and Independents.
The counting of votes relating to all the 30 segments is expected to be completed by 11 PM Sunday, a release from the office of CEO said.
The chief contestants in the poll are the AINRC leader N Rangasamy heading the NDA in which the AINRC, AIADMK and Bharatiya Janata party (BJP) are the constituents.
On the other side, the Congress-led Secular Democratic Alliance (SDA) comprises the Congress, DMK, VCK and CPI.
Former Congress Ministers M O H F Shah Jahan, M Kandasamy and R Kamalakannan are the chief contestants on behalf of SDA.
Former Chief Minister and senior Congress leader V Narayanasamy opted out of poll battle.