Dozens of activists died when Poland's last communist leader Gen Jaruzelski cracked down on dissidents.
Hours before the rallies, the leader of the ruling centre-right Law and Justice party, Jaroslaw Kaczynski, branded the current opposition as "anti-state".
He went on to threaten to "bring order" to opposition activity.
Mr Kaczynski, widely seen as the power behind Poland's government, did not specify what he had in mind during a radio interview. Addressing a pro-government rally later, he ridiculed opponents for resisting plans to change a system which he said had harmed the majority of Poles.
However, the Committee for the Defence of Democracy (KOD) commemorated the anniversary of martial law with anti-government marches across the country, and a large crowd snaked through the centre of Warsaw.
Protesters highlighted government policies on women's rights as well as reforms to education and the top legislative court.
Many members of Poland's current governing Law and Justice (PiS) party were part of the opposition Solidarity movement, which the communist regime set out to crush under martial law.
Thirty-five years on, Poland's opposition leaders say PiS, and its head Jaroslaw Kaczynski, are behaving as badly as the communists, restricting democratic freedoms and hobbling the Constitutional Tribunal so it is unable to veto the government's programme.
Mr Kaczynski says the opposition refuses to accept PiS's victory in last year's elections and its continuing popularity, branding the accusations "absurd".
Simple comparisons to the communists are overblown, of course, but Mr Kaczynski continues to give more liberal-minded Poles cause for concern, branding them "anti-state" and warning that the government plans to introduce measures to bring "order" to the opposition's activities.
Gen Wojciech Jaruzelski argued that he had imposed martial law on 13 December 1981 to deter a Soviet invasion.
But in the subsequent crackdown, thousands of members of the pro-democracy Solidarity movement were arrested and as many as 100 people died. Martial law was lifted two years later and Gen Jaruzelski eventually stood down in 1990. He died in 2014.
Poland's defence minister said on Tuesday that the government would act to strip the late general and his late deputy, Gen Czeslaw Kiszczak, of their military ranks.
Poles have marked the 1981 imposition of martial law with marches, and thousands used the occasion to protest against the conservative government.