Election observers said any reliable indication of the winner could take as long as a week.
By mid-afternoon on Tuesday, Megawati's Indonesia Democratic Party-Struggle (PDI-P) led with 19%, followed by the party of former president Abdurrahman Wahid with 18%. Golkar, the former political vehicle of ousted autocrat Suharto, was third, with 15%.
The result of Monday's election in the world's most populous Muslim nation will shape the race for the country's first direct presidential vote in July.
With no candidate likely to win a majority in that election, coalition-building will be crucial in the run-up to the vote.
"This is all a pre-run for the presidential race," said chief European Union election observer Glyn Ford.
"We don't expect any meaningful information for probably five to seven days," said Hank Valentino of the US-based International Foundation for Election Systems. He said urban areas would be tallied first, skewing initial results.
"The General Election Commission has been saying a final result is going to take 21 days. The law says they have 30 days," Valentino said. He said voter turnout from the 147 million strong electorate was thought to have been above 90%.
The trickle of results harks back to the last election in 1999 when the full count took weeks.
"We don't expect any meaningful information for probably five to seven days"
International Foundation for Election Systems
Most opinion polls before Monday's vote showed Golkar likely to unseat Megawati's party as the largest in parliament, although without a majority, as many yearn for the firm leadership and economic growth of Suharto's 32-year rule.
They also showed the incumbent president trailing her former security minister, Susilo Bambang Yudhoyono, in the presidential race.
Yudhoyono's Democrat Party was running fourth in the early election count, a strong showing given its status as a new party.
Monday's elections for the 550-seat parliament and local legislatures went off largely peacefully and were billed as history's biggest one-day vote. It was only the second democratic poll since Suharto's fall in 1998.