The squabble comes as Lai Ching-te took office on Monday as the new president, facing not only an angry China, which views him as a "separatist", but also a fractured parliament, after his Democratic Progressive Party (DPP) lost its majority.
Several hundred people gathered outside parliament to protest against the reforms, and accused the opposition of working in concert with China and trying to kill democracy.
The two main opposition parties, the Kuomintang (KMT) and Taiwan People's Party (TPP), which together have enough seats for a majority, have joined hands to back reforms that give parliament greater scrutiny over the government.
That includes a controversial proposal for lawmakers to punish officials deemed to commit contempt of parliament by making false statements or "withholding information", which the DPP says lacks a clear definition.
While there was no repeat of Friday's scenes of legislators punching and wrestling each other in the chamber, DPP lawmakers wearing headbands reading "Democracy has died" demanded more discussions on the proposals and vented their anger at the KMT.
"On the speaker's platform today is not the KMT or the TPP. It's Xi Jinping," DPP caucus whip Ker Chien-ming told the chamber, referring to China's president.
His remarks prompted shouts of "Shut up!" from the opposition camp, some of whom brandished signs reading, "Reforming parliament, let sunshine in."
The KMT accused the DPP of trying to "spread rumours and paint them red", the colours of China's ruling Communist Party, in a bid to stifle the reforms.
"The DPP is stirring up populism, and their anti-reform actions don't have a leg to stand on," said KMT spokesperson Yang Chih-yu.
Taiwanese drag queen Nymphia Wind, the winner of this year's RuPaul's Drag Race, appeared briefly at the protest rally to offer support.
"I respect parliament, but I hope parliament can do things that we respect and respect our democratic procedures," she said. "As a Taiwanese citizen, I think we must stand up."
The current reform proposals "overly expand" the power of the lawmakers, Chang Hung-lin, the head of Citizen Congress Watch, a non-government group advocating for citizen supervision of parliament, told Reuters, although the group backs an existing effort to give parliament more government oversight. The current proposals, some of which passed a second reading on Tuesday, give lawmakers the right to demand parties such as defence officials and private companies testify in parliament without proper checks and balances, he said.
"This is harmful to our administrative power and the judiciary," he added.
