"For the moment, the question of the treaty is pointless," he said.
Although the Polish parliament ratified the treaty in April, it still needs the signature of the president.
The BBC's Adam Easton in Warsaw says Mr Kaczynski's comments are unsurprising as he is opposed to deeper European integration.
Our correspondent says the president would be happy to see the Nice Treaty, which currently governs the way the EU operates and gives Poland disproportionate strength, remain in force for a while longer.
However, he is in conflict with Prime Minister Donald Tusk, who has said the EU will find a way to bring the treaty into force.
Ireland's 'No' vote delivered a huge blow to the Lisbon Treaty
Mr Tusk said: "I hope the president will re-consider this position. I have no doubt that the treaty's ratification is in Poland's best interest."
Mr Kaczynski has joined his Czech counterpart in openly opposing treaty ratification.
Czech President Vaclav Klaus, and many lawmakers, do not want to sign the treaty while its future is still uncertain.
German President Horst Koehler has also delayed ratification - until the country's highest court has delivered a ruling on legal challenges.
Mr Kaczynski warned EU members not to pressure Ireland to find a solution.
"If one breaks the rule of unanimity one time, it will never exist again," he said.
However, the president did say he thought the EU would carry on working. "Certainly it isn't ideal, but a structure this complicated couldn't be ideal," he said.
There will be a ceremony at the Arc de Triomphe in Paris on Tuesday to mark the beginning of France's six-month presidency, which it takes over from Slovenia.
But Mr Kaczynski's comments will mark a difficult opening to the French stint.
President Sarkozy expressed his concerns in an interview on French television channel France 3.
Mr Sarkozy said: "Something isn't right. Something isn't right at all."
The Eiffel Tower is illuminated as France takes over the EU presidency
"Europe worries people and, worse than that, I find, little by little our fellow citizens are asking themselves if, after all, the national level isn't better equipped to protect them than the European level," he added, calling such thinking a "step backward".
Mr Sarkozy said: "The first priority is to pinpoint the problem with the Irish voters and to continue to allow other countries to be ratified, especially our Czech friends."
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