Udar party leader Vitali Klitschko was among those critics of President Viktor Yanukovych and his ruling allies who issued the appeal on December 29 on Independence Square in Kiev, which has been the hub of pro-EU protests for a month.
Klitschko said authorities expected the "Euromaidan" protests that erupted after Yanukovych's government suspended talks on an Association Agreement ahead of a major EU summit in late November.
"They expect us to tire and go home," Klitschko told the crowd, according to RFE/RL's Ukrainian Service.
"But no, we will fight to the bitter end. We will not go away."
The crowd numbered in the tens of thousands but was seemingly down from previous weeks.
The parliamentary opposition signaled its commitment to keeping the political pressure on the ruling parties until Ukraine's next scheduled elections in 2015.
"We are preparing to win the presidential elections," Arseny Yatsenyuk, the leader of the opposition Fatherland (Batkivshchyna) party told the rally.
"We are building a team...that will be able to turn Ukraine into a European country."
Yatsenyuk also drew a connection between the ongoing protests and a recent brutal attack on a Ukrainian journalist and activist for which five suspects have been arrested.
"We have named our today's rally 'Solidarity Against Terror' -- against the terror that was unleashed by the authorities when they attacked Tetyana Chornovil with these thugs outrageously beating her; against the terror that sees 'Euromaidan' activists prosecuted and intimidated by the current political machinery; against the terror directed against those families that now see their children afraid to go to school," Yatsenyuk, a former close ally of jailed former Prime Minister Yulia Tymoshenko, said.
Some Ukrainian motorists meanwhile demonstrated on a road near Yanukovych's Kiev residence, honking car horns and generally slowing traffic before heading toward the home of pro-Russian strategist Viktor Medvedchuk, who heads the Ukraine's Choice civic movement.
There were no reports of arrests or violence.
The protesters are demanding the punishment of those responsible for the forcible dispersement of peaceful protests that attracted hundreds of thousands in the days after the EU snub, the release of people detained in connection with the demonstrations, and the dismissal of the Ukrainian government.
Ukraine, which is predominantly Orthodox, marks Christmas with a public holiday on January 7.
Source: Radio Free Europe