Mr Kaczynski had delayed signing pending the Irish referendum result
Fresh doubts have arisen about Poland's expected ratification of the EU's Lisbon Treaty, after contradictory messages about the president's plans.
President Lech Kaczynski's twin brother Jaroslaw has now denied that the president will sign the treaty on Sunday, as announced earlier.
The twins are political allies, and Jaroslaw heads the main opposition party, Law and Justice (PiS).
Poland and the Czech Republic are the only EU states yet to ratify Lisbon.
The treaty cleared a major hurdle on 2 October when voters in the Republic of Ireland backed it overwhelmingly, in a second referendum. Lisbon is aimed at streamlining EU institutions.
President Kaczynski, a Eurosceptic, had said he would wait for the Irish voters' verdict before signing the treaty.
"According to what I know, and I have knowledge of this, this won't happen on Sunday," his brother Jaroslaw told a news conference on Thursday.
He was speaking shortly after a top aide to Lech Kaczynski had said the president would sign the treaty on Sunday. Lisbon has already been approved by the Polish parliament.
"The president keeps his word. He said he will sign the treaty with no delays if the Irish say 'yes'. On Sunday he will sign the treaty," presidential aide Aleksander Szczyglo told Poland's TVN 24 channel.
Unlike Mr Kaczynski, Prime Minister Donald Tusk and his centre-right government strongly support Lisbon.
EU leaders are anxious to get the treaty fully ratified this year - well before UK elections next spring, which could see a triumph for Conservative leader David Cameron. Many in his party oppose Lisbon and are demanding a referendum on it.
EU governments see the treaty as fundamental to the 27-nation bloc's future success. Without it, they argue, the EU's decision-making processes will remain slow and cumbersome, because they date back to when the EU consisted of only 15 nations.
Opponents see Lisbon as part of a federalist agenda that threatens national sovereignty.