"My dream of becoming prime minister has faded away," said Rajapaksa. "I am conceding. We have lost a good fight," reported AFP.
Rajapaksa accepted that his United People's Freedom Alliance (UPFA) had lost even before Elections Chief Mahinda Deshapriya could announce the final results.
"We have won eight districts and the UNP (ruling United National Party) has 11 (out of a total of 22)," Rajapaksa said. "This means we have lost. It was a difficult fight."
No party appears to have secured an absolute majority of 113 seats in the 225-member parliament, which will force the new government to seek out smaller allies.
Election Commissioner Deshapriya said he expected the release of the final party positions by midday Tuesday, while individual votes garnered by candidates would be announced later.
Parliamentary elections were held in Sri Lanka a year ahead of schedule by President Maithripala Sirisena who ousted the veteran leader Rajapaksa in January this year.