Mr Premadasa came in second with about 26% of the total vote. President Ranil Wickremesinghe, who is seeking a second term, has so far received 16%, while Namal Rajapaksa, the ousted president’s nephew, is close to 3%.
17 million Sri Lankans are eligible to vote on Saturday.
The vote was peaceful, but authorities declared a curfew on Sunday morning, which was extended until noon local time (00:630 GMT).
Dissanayake has already received congratulatory messages from supporters of his two main rivals, incumbent President Ranil Wickremesinghe and opposition leader Sajith Premadasa.
Foreign Minister Ali Sabri said early results from X clearly showed a victory for Dissanayake.
“I campaigned a lot for President Ranil Wickremesinghe, but the people of Sri Lanka have made the decision and I fully respect their mandate for Anuradhapura Dissanayake,” he said.
MP Harsha de Silva, who supported Premadasa, said he had called Dissanayake to congratulate her.
“We campaigned hard for @sajithpremadasa but it didn’t happen. It is now clear that @anuradisanayake will be the new President of #SriLanka,” said de Silva, who represents Colombo in parliament.
Another Premadasa supporter and Tamil National Alliance (TNA) spokesman MA Sumanthiran said Dissanayake had achieved an “impressive victory” without resorting to “racial or religious chauvinism”.
