Sri Lanka's strongman Mahinda Rajapaksa was poised to stage a political comeback on Thursday as his party took an early lead and was set for a landslide victory in the twice-postponed general elections, according to results announced so far.

Prime Minister Narendra Modi was among the first world leaders to congratulate Rajapaksa on the outcome of the elections and said the two sides will work together to further advance all areas of bilateral cooperation and to take their special ties to ever newer heights.

"Thank you PM @narendramodi for your congratulatory phone call. With the strong support of the people of #SriLanka, I look forward to working with you closely to further enhance the long-standing cooperation between our two countries. Sri Lanka & India are friends & relations," Rajapaksa tweeted.

The SLPP has polled more votes than its rivals, scoring over 60 per cent of the total votes in the 16 seats officially declared so far from the South, dominated by the Sinhala majority community. The party won 13 out of 16 seats.

President Gotabaya Rajapaksa in a tweet described the results as a "great victory" for the ruling party.

Rajapaksa's party is expected to win control of the 225-member assembly by a comfortable margin, according to analysts.

In Galle district, the SLPP won seven out of nine seats on offer while in the neighbouring Matara district they won six out of seven seats on offer.

The nearest rival is the new party formed by former presidential candidate Sajith Premadasa who has relegated his mother party, the United National Party (UNP), of former premier Ranil Wickremesinghe to the fourth place even below the Marxist Janatha Vimukthi Peramuna (JVP).

The SJB has won only three seats from both districts.

In the polling division results from other districts where counting is in progress, the SLPP has taken unassailable leads, sources said.

In the Tamil minority dominated north, the main Tamil party - Tamil National Alliance (TNA) - despite bagging a few polling divisions had also suffered unexpected reversals at the hands of SLPP's Tamil allies - the Eelam People's Democratic Party (EPDP).

The counting began in the morning after the polls were closed on Wednesday.

As the counting of votes began, SLPP founder and its National Organiser Basil Rajapaksa -- who is the younger brother of President Gotabaya Rajapaksa with the eldest being Prime Minister Mahinda Rajapaksa -- said that the party is all set to form a new government.

President Gotabaya hopes for a two-thirds majority for the SLPP so that he can amend the Constitution to restore presidential powers curbed by a 2015 constitutional change.

The president is not a candidate while care-taker prime minister Mahinda is running from the north western capital district of Kurunegala.