Crowds gathered outside the presidential palace on Saturday morning and then marched to parliament.
Inside parliament itself, opposition MPs have continued a sit-in that began on Friday.
Polish Prime Minister Beata Szydlo, in a televised address, called the MPs' actions "scandalous".
She said people were free to protest, but had to respect the views of others.
Poland's populist right-wing government wants to limit the number of reporters allowed to cover parliament.
But opposition MPs accuse it of trying to stifle press freedom.
Amid a heavy police presence, a crowd of about 2,000 people gathered outside the presidential palace on Saturday chanting "freedom, equality, democracy". Some held up copies of the constitution.
The crowd later marched to the parliament building where they remained throughout the day.
European Council President Donald Tusk, a former Polish prime minister, urged the government to respect the constitution on Saturday.
Addressing reporters in the western city of Wroclaw, he criticised the government's plans, saying that without media access "democracy becomes dictatorship".
In extraordinary scenes on Friday, opposition MPs blockaded the parliamentary plenary chamber, forcing MPs from the PiS party into another room to vote on next year's budget.
It was the first time since the restoration of democracy in 1989 that such a vote was held outside the main chamber of parliament.
Outside parliament, several thousand protesters gathered overnight on Friday. Police had to forcefully remove people to allow MPs to leave the building.
Protester Szymon Roginski said on Saturday that the confrontation was entering "a new, more aggressive phase".
"Every day we hear news that makes us understand that we are further and further away from democracy. People have had enough," he said.
Leader of the opposition Nowoczesna party, Ryszard Petru, accused the government of usurping parliament's authority.
"They [the government] do not allow journalists [access], they close themselves off and meet in other places and call it the parliament," he said.
"This is an usurpation of power and there will be no consent from the opposition or Polish society for it. We will protest both at the parliamentary podium and on the streets of Polish cities."
PiS has been accused of restricting press freedom since coming to power last year.
Next year only a few reporters will be allowed into parliament, with five selected TV stations permitted to make recordings of parliamentary sessions.
PiS leader Jaroslaw Kaczynski said on Friday that the proposals were no different to the media access in many other European nations.
He accused protesters of hooliganism and threatened them with unspecified "consequences".
Demonstrators in the Polish capital Warsaw have renewed their protest against government plans to restrict journalists' access to parliament.