"I ask you to be calm and patient in waiting for the result," Megawati said in a brief statement on Thursday at the presidential palace. "Let it flow, because it's the people's will that counts."
Tabulation has gone slowly as returns trickle in from the vast archipelago, despite optimistic forecasts before the vote that the count would be relatively swift.
Investors have shrugged off the slow count, taking solace in the relatively peaceful voting and expectations that pro-business parties will win.
The Jakarta stock market closed at a four-week high on Tuesday and was marginally higher on Wednesday afternoon, while the rupiah was holding firm.
The latest numbers showed Megawati's party ahead, although the 37 million votes counted by midday on Thursday comprise just 25% of the 147 million people eligible to vote in the world's fourth most populous country.
The performance of the 24 parties fighting Monday's election is expected to shape the race to win the presidency in a direct vote on 5 July.
"We should be proud that we can conduct it peacefully and democratically"
By midday Megawati's Indonesia Democratic Party-Struggle (PDI-P) had 21%, against 20% for Golkar, the former political vehicle of ex-strongman Suharto.
In third place was the National Awakening party, led by former president Abdurrahman Wahid, with 14%. The other 21 parties were all at single-digit levels.
But the showings could easily change as results from various parts of the country arrive at different speeds.
However, many observers have been impressed simply by the fact that what was described as the biggest and most complex election held on one day went off peacefully in a country hit by deadly ethnic and sectarian violence in recent years.
The election was Indonesia's second since the fall of autocrat president Suharto in 1998. "We should be proud that we can conduct it peacefully and democratically," Megawati said.
Glyn Ford, chief of a European Union observer mission, said that, despite some glitches: "5 April marked an important step in the consolidation of Indonesian democracy.
"The process culminating in election day was credible and had integrity," he told reporters.