He also pledged a government that would provide for economic stability and development.
Kaczynski has also indicated that his government will be largely a continuation of the coalition of conservatives, populists and nationalists that resigned on Monday along with Prime Minister Kazimierz Marcinkiewicz.
Kaczynski told reporters his Cabinet could take office by the end of the week.
He has 14 days to build a Cabinet, and another two weeks after that to face a confidence vote in parliament. Government spokesman Jan Dziedziczak said Tuesday that Kaczynski will meet "with candidates for ministers of his Cabinet." Only one or two posts - including that of finance minister - are expected to change from the outgoing government.
Marcinkiewicz resigned amid reports of disagreements over economic policy between him and Kaczynski, who was widely regarded as the power behind the scenes of the outgoing government. He is now to become the party's candidate for mayor of Warsaw, the AP reports.
Kaczynski has said his future Cabinet would continue the pro-social welfare policies of Marcinkiewicz's government. Law and Justice sealed a coalition deal in May with two Euro-skeptic parties - the farm-based Self-Defense and the Roman Catholic League of Polish Families.
Kaczynski's identical twin brother Lech was elected president last October, a month after the brothers' Law and Justice party won parliamentary elections in September.
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First Deputy Minister of Information of the Donetsk People's Republic Daniil Bezsonov showed the video of an ammonia cloud that appeared after the Armed Forces of Ukraine shelled the Togliatti-Odessa ammonia pipeline