"I have a very concrete offer for PO (Civic Platform). I will present a modified economic programme today," Kazimierz Marcinkiewicz from the conservative Law and Justice (PiS) party said in a radio interview with privately owned RMF-FM.
The programme, which Marcinkiewicz was due to present at a press conference at the Warsaw stock exchange at 3:00 pm (1300 GMT), would introduce two rates of personal income tax, one corporate tax rate and two VAT rates, he said.
The PO campaigned in last month's legislative election on a single, across-the-board rate of taxation, pegged at 15 percent.
PiS, which won 155 seats in the 460-seat parliament against the second-placed PO's 133, proposed a two-tiered tax system.
"The flat tax is very difficult to introduce," Marcinkiewicz said, adding that his new proposal envisaged lower taxes and a simplified system. There are currently three tiers of tax on personal income in Poland, and one for companies.
The health service proposal that Marcinkiewicz would put forward was a happy medium between the "rather revolutionary PiS and PO programmes", he added.
If his conciliatory offer did not convince PO to join PiS in a coalition, Marcinkiewicz said he had another set of proposals which he would put forward on Monday, his self-imposed deadline for naming a government.
Coalition talks ground to a halt Wednesday when PO leader Donald Tusk accused PiS of striking a deal with the populist, eurosceptic Samoobrona and the far-right League of Polish Families (LPR) to block the election of PO's candidate for the key post of lower house speaker.
The coalition talks were already in jeopardy, with PO accusing PiS of hoarding power and unfairly distributing cabinet seats.
On Thursday, PiS then blocked PO's candidate for one of five deputy speakers' seats in the upper house Senate.
In an interview with public station Radio One, PO lawmaker Hanna Gronkiewicz-Waltz said that while Marcinkiewicz was saying one thing, PiS leader Jaroslaw Kaczynski and his twin Lech, who on Sunday confounded polls by beating Tusk in a presidential election, were doing the opposite.