Mr Kaczynski made his pledge during a policy speech in parliament that preceded a vote by lawmakers to approve or reject his government program, the final step before he and his cabinet formally take office.
Mr Kaczynski, head of the conservative Law and Justice (PiS) party, was sworn in by his twin brother President Lech Kaczynski last week, following the surprise resignation of prime minister Kazimierz Marcinkiewicz.
"We are going to work for EU enlargement to mean real participation, not just formal participation (of new member states) in all decision-making mechanisms," Jaroslaw Kaczynski told deputies.
He said he wanted Poland to become a "big country that counts" in Europe.
He pledged that his country would strive for a stronger voice "on our own but also with the Weimar Triangle" states, which in addition to Poland include France and Germany, and the Visegrad group, made up of the Czech Republic, Hungary, Poland and Slovakia.
All four Visegrad countries joined the EU in May 2004.
The prime minister also vowed to defend overwhelmingly Catholic Poland's moral values within the EU, particularly the notion that "marriage is a union between a man and a woman."
"We will do everything to defend the Polish family against all attacks, in particular from outside," he said in an apparent reference to European politicians who supported a gay rights march in Warsaw in June.
"We will demand full sovereignty in moral matters," Mr Kaczynski added, insisting that Poland would "preserve its moral national identity" within the EU.
The prime minister also confirmed that his new government would make reforms to the country's public finances a top priority.
Although he admitted that there could be delays in plans which had envisaged the reforms being implemented still this year.