The state electoral commission on Sunday said that with 32% of the ballots counted, Tusk had a narrow lead with 35.4% of the votes and Kaczynski 32.9%. Turnout was almost 50%.
Such a final result would force the two former activists with the anti-communist Solidarity movement into a head-to-head race on 23 October.
Final official results were not expected until about 6pm (1600 GMT) on Monday, the state electoral commission told The Associated Press.
Economy v. safety net
An exit poll by state television indicated Tusk, who wants to stimulate the economy with low taxes and deregulation, led with about 38% while Kaczynski, a former child actor hoping to preserve a strong safety net, had 32%.
The race centred on the Europe-wide issue of just how far to go in sacrificing welfare state protections for the promise of an American-style economy with fewer social benefits but faster growth and job creation.
Donald Tusk (above) faces Lech
Kaczynski (below) on 23 October
Tusk wants a 15% flat tax rate on personal and corporate earnings, while Kaczynski favours a greater role for the state in protecting the social safety net and promoting Roman Catholic values. He wants tax cuts, but would keep the system under which high earners pay more - and would give deductions for big families.
The election of either candidate would cement the sharp decline of the ruling former communists, who were defeated in parliamentary elections on 25 September after a series of sleaze scandals and failure to slash Poland's jobless rate, now at 17.8%, the highest in the European Union.
Among a field of 12, Andrzej Lepper, leader of the farm-based Self-Defence party, came third with 13.2%, according to the exit poll. Marek Borowski, a former communist, had 10.2%, a showing that was slightly better than opinion polls had predicted.