Kaczynski, who won Sunday's presidential run-off and views the United States as the main protector of Poland's security, said on Monday the decision depended on what Washington had to offer in return.
"We have to clearly say that Poland is generally pleased with having taken part in the Iraqi mission. We proved to be a dependable ally, a country able to act in different parts of the world, which is very important," he said.
"As a loyal ally of the United States we must know on what conditions could this mission be extended," he added.
Kaczynski said he spoke briefly with US President George Bush earlier on Monday. Bush congratulated the Warsaw mayor, the White House said.
Kaczynski declined to say what he would like from Washington in exchange for continued Polish support in Iraq, where the country has about 1700 soldiers, which helps to maintain the multi-national character of foreign forces stationed there.
After meeting Bush in Washington earlier this month, outgoing President Aleksander Kwasniewski said Poland would keep troops in Iraq through January, adding the new government would have to decide the course for the future.
Poland's outgoing leftist administration backed the US-led invasion of Iraq, initially contributed 2500 troops and took command of one of four "stabilisation zones" in the country.
Despite popular opposition for sending troops to Iraq, Warsaw says the move is a necessary part of the global "war on terror". Analysts say it raises Warsaw's international clout.