Walesa is seeking an apology and more than $30,000 in damages, The Daily Telegraph reported.
Kaczynski, on television, said Walesa gave information to government spy agencies under the code name Bolek. Walesa in turn told an interviewer he would "get" Kaczynski.
Lawyers for the two men were in court Tuesday for a preliminary hearing.
Kaczynski and his twin brother, Jaroslaw, who served as prime minister from July 2006 to November 2007, were members of Solidarity, the movement led by Walesa. But a rift developed soon after Walesa became president of Poland in 1990.
"For the Kaczynskis, he is the main enemy and a symbol of what has been wrong with Poland since 1989," Jacek Kucharczyk of the Institute of Politics said.
Walesa says he has already been cleared of being a Communist agent. Such charges are often murky because Communist spy agencies often created false documents to smear opposition leaders.