The report was unveiled at a ceremony in Warsaw exactly 83 years after Nazi Germany invaded Poland to start the war, Polish state news agency PAP reported.
Kaczyński told the gathering at Warsaw's Royal Castle that "a decision has been made to demand reparations" from Germany.
He said: “It’s about securing compensation, maybe through a long and arduous process, for everything that Germany, the German state, the German nation, did to Poland between 1939 and 1945.”
Meanwhile, Prime Minister Mateusz Morawiecki said the new publication could help bring about "genuine reconciliation, repair of Polish-German relations."
He added: "Without truth, reparations, compensation, there can be no genuine relations between people, states, nations."
Report estimates Poland's WWII losses at PLN 6.2 trillion
According to the three-volume report, compiled over five years by a team of 30 historians, economists and appraisers, the damage inflicted on Poland by Nazi Germany during World War II totals PLN 6.2 trillion (EUR 1.3 trillion) in today's money, officials said.
"The sum that was presented was adopted using the most limited, conservative method," Kaczyński, who leads Poland's ruling conservative Law and Justice (PiS) party, told a news conference.
"It would be possible to increase it," he added.
Cost of WWII
Around 6 million Poles, including 3 million Polish Jews, were killed during World War II, and the capital Warsaw was levelled following a 1944 uprising in which about 200,000 civilians died, the Reuters news agency reported.
However, in 1953, Poland's then Soviet-controlled government relinquished all claims to war reparations under pressure from Moscow, which wanted to free East Germany, also a Soviet-controlled country, from any liabilities, according to officials.
Poland’s governing conservatives say the 1953 agreement was invalid because Warsaw was unable to negotiate fair compensation.
Sixty-four percent of Poles believe Germany should pay reparations for the damage it caused to Poland during World War II, according to a survey published in July.
Source: PAP, Reuters, polskatimes.pl