Kaczorowski's tomb in a Warsaw church and the grave of another victim were opened to allow investigators to compare the two sets of remains, amid claims they were switched by mistake.
"Doubts about the identity of the bodies which arose in legal documents have led military prosecutors to exhume them," prosecutor's office spokesman Zbigniew Rzepa told AFP.
"At the family's request, we can't reveal the identity of the exhumed individuals," he added.
Polish media reported that one of the bodies was thought to be that of Kaczorowski, the last president of the London-based exiled government which was set up during World War II and remained in existence until Warsaw's post-war communist regime crumbled in 1989.
Rzepa said at least two other bodies were due to be exhumed.
Last month investigators confirmed that the body of 1980s anti-communist opposition icon Anna Walentynowicz a founder of the Solidarity trade union had been switched with that of another crash victim.
Walentynowicz was subsequently reburied in the grave that had carried her name, and her new funeral had a highly political edge.
Poland's conservative opposition leader Jaroslaw Kaczynski identical twin and political ally of Lech Kaczynski has repeatedly accused the country's centrist government of failing to hold Russia to account for the crash.
The presidential jet crashed on April 10, 2010 as it tried to land in fog at the airport in Smolensk, western Russia, ahead of a ceremony marking the 70th anniversary of the Soviet slaying of thousands of Polish prisoners of war.
All 96 people on board died, and while pilot error and the aging facilities at the airport were ruled to be behind the crash, many in Poland give credence to conspiracy theories blaming age-old foe Moscow.