Michael Sata had a clear lead on Friday after early results gave his Patriotic Front party about three-quarters of the first seats to be declared. But political observers have said the final result could remain close.
The independent Zambia Post newspaper reported large wins overnight for Levy Mwanawasa which could yield a "landslide win" for the current president and his Movement for Multiparty Democracy.
The newspaper said it projected that Mwanawasa's party could emerge with as many as 81 of the parliament's 150 seats, up from the 72 it won in 2001.
Sata has conceded that he might not control parliament, but told the Post that he was still confident he would win the presidency.
"Yes, they can get their 81 seats but they will not get the presidency," Sata said. "Tell Levy that if they play some monkey tricks, the consequences will be too ghastly for them to contemplate".
Chief Justice Ireen Mambilima, head of the elections commission, had announced on Friday that Sata was comfortably ahead of Mwanawasa in the presidential race after results had been confirmed in 26 constituencies.
Sata had 49 per cent of the first 721,923 votes to be counted, while Mwanawasa trailed behind with just 28 per cent.
Early results put Sata ahead in
the presidential race
Mwanawasa ran for a second term as president based on his strong economic record, which has included securing billions of dollars in debt relief and boosting economic growth, but he has little of Sata's popular appeal.
Sata - nicknamed "King Cobra" - has promised to cut taxes, build thousands of low-cost homes and embark on a massive job creation scheme during his first 90 days in office.
Tensions have been growing due to delays in getting the election results. Polling was extended in some areas of the country and it is unclear when the final count will be announced.