At a ceremony in Krasnik, eastern Poland, Blaszczak said the new law on homeland defence, which introduced the one-year-long service on a voluntary basis, was "an important event for the Polish armed forces."
Poland suspended mandatory conscription in 2010 in order to professionalise its armed forces.
"We all know perfectly well what's happening behind our eastern border and we are aware of the threats," he said. "These threats are real: Russia has attacked Ukraine and there is a war going on behind our border."
According to Blaszczak, the best response to the threats is to strengthen the Polish military.
"This is why we decided to start a campaign of voluntary basic military service," he said.
"Our goal is to increase the number of soldiers in the Polish armed forces to 300,000, including 250,000 professional soldiers," Blaszczak went on to say. "We also want as many people as possible to be trained and to have vast numbers of reservists who know how to behave in a crisis situation and who can handle weapons."
According to the government, Poland now has about 111,500 professional servicepeople and 32,000 territorial defence soldiers.
Recruitment to the service was launched on Saturday, with military picnics organised in 32 Polish cities and towns. Poland has also prepared 70 recruitment stations.
Those who want to join the military have three options now. They can become professional soldiers, decide to do basic military service or join the territorial defence force. (PAP)