Jaroslaw Kaczynski, leader of opposition party Law and Justice, used a march marking the imposition of martial law 33 years ago to repeat claims that November's local elections were rigged.
''Those elections were falsified,'' Kaczynski declared at the conclusion of Saturday's march, which was attended by 60,000 people, according to organisers.
''The authorities are rejecting proposals for changes [to the law],'' he added.
''There will come a day when the elections will be repeated,'' he said.
The gathering, dubbed by organisers ''the march in defence of democracy and a free media'', continued Law and Justice's tradition of hosting a march on the anniversary of the then communist regime's imposition of martial law on 13 December 1981.
Although Law and Justice narrowly won the highest percentage of votes in the 16 November elections to Poland's regional assemblies, an exit poll had given the party a 4 percent higher victory.
Law and Justice claim that the high level of invalid votes (17.8 percent), indicates foul play.
Over the last 15 years, the previous record for invalid votes for regional assemblies was 14.4 percent (2002), although no claims were made then of rigging. In 2010, the level was 12 percent.
Those rejecting the theory of foul play argue that the high levels of invalid votes are because Poles are more interested in the simultaneous voting for mayors. Traditionally there are significantly lower levels of invalid votes in these elections, which are held on the same day.
Earlier in the march, Kaczynski stressed the importance of remembering the dozens of opposition activists who died as a result of repressive measures during martial law, which lasted from 13 December 1981 to 22 July 1983.
''This remembrance is necessary so that Poland can be democratic,'' he said.
Prime Minister Ewa Kopacz said that she is ''outraged'' by what she claims is ''the cynical exploitation of 13 December.''