If the trend holds, Kumaratunga, who is elected separately, will have a friendly government to deal with, but would still face problems restarting a stalled peace process with the island's Tamil Tiger rebels.
The Elections Commission said that with more than one-third of the votes counted, Kumaratunga's United People's Freedom Alliance had 44% of the vote against 33.8% for Prime Minister Ranil Wickremesinghe's United National Party (UNP).
It is not clear yet how many seats that will translate into. But projections by The Lanka Academic website (theacademic.org) show the Alliance taking about 106 seats, down from an earlier predicted 111, in the 225-member parliament. The UNP is forecast to take about 87 seats.
Most peaceful poll
The vote in one of Sri Lanka's most peaceful elections in decades was fought mostly over how to permanently end the 20-year civil war that has killed 64,000 people.
A ceasefire that Wickremesinghe signed more than two years ago has been jeopardised by stalled peace talks, the feud between the president and prime minister and a recent split in the ranks of the Tamil Tigers.
Security was tight as the last
poll in 2001 was very violent
The election result is also critical for the economy, which grew by an estimated 5.5% last year. The stock market has surged nearly 80% since the ceasefire was signed in February 2002 as prospects of a peace dividend lured investors back and aid donors pledged $4.5 billion.
Kumaratunga called the election nearly four years early after accusing Wickremesinghe of being too soft on the rebels.
Time to convince
If the Freedom Alliance is short of a majority, Kumaratunga has until parliament opens on 22 April to convince several minor parties to support her, including a party of Buddhist monks projected to win seven seats.
The Liberation Tigers of Tamil Eelam (LTTE) has said it will resume negotiations with anyone who has a mandate and the power, but the rebel split, with a strong eastern commander breaking away last month, may complicate that.
An LTTE-backed party, the Tamil National Alliance (TNA), could win up to 19 seats.
Wickremesinghe has notched
33.8% of vote thus far
The People's Liberation Front, one of the main partners in the Freedom Alliance, has in the past opposed making any concessions in dealing with the LTTE.
Kumaratunga began the current peace process in 2000 by inviting Norwegian mediators, but was unable to agree on a truce or on starting talks - something Wickremesinghe was able to do.
Unlike previous polls, including the last in 2001 when 25 people were murdered on election day, Friday's vote was mostly violence free.
Three-quarters of the nearly 13 million eligible voters cast their ballots, including Tamils living in rebel-held areas, but turnout was only 60% in the east where a split in the rebel ranks has raised security worries.
It was the first time the rebels had endorsed a party, but there were allegations of election fraud in Jaffna in the Tamil-dominated north - the Tigers' stronghold - where the TNA won 90% of the vote at some polling stations.
The Tigers began fighting more than two decades ago for a separate homeland in the north and east for minority Tamils, who say they are discriminated against by the Sinhalese majority.
The Tigers control a swathe of territory in the north and east, but have dropped a long-standing demand for a separate Tamil state in favour of autonomy.