TAIPEI - Tens of thousands of people took to the streets around Taiwan's parliament on Friday to demonstrate against contested parliamentary reforms, in a protest also marked by anger over China's perceived influence on the island's democracy.

The rally outside parliament, following one on Tuesday, came on the same day China, which claims Taiwan as its own territory, carried out a second day of war games around the island Beijing has said were launched to punish Taiwan's new president, Lai Ching-te, who it calls a "separatist".

Lai's Democratic Progressive Party (DPP) is trying to stop the opposition, who together have a majority of seats in the parliament, from forcing through measures to give lawmakers more oversight over the government. The DPP says more debate is needed.

The reforms will give lawmakers the power to ask the military, private companies or individuals to disclose information deemed relevant by parliamentarians.

They will also criminalise contempt of parliament by government officials and make the offence punishable with prison terms. But the DPP says there is no clear definition of contempt of parliament.

Taiwan's main opposition party the Kuomintang (KMT), which supports closer ties with China but denies being pro-Beijing, says it is trying to bring more accountability to government.

Friday night's protesters, many of them students or young professionals, listened to speeches and carried banners accusing the opposition of trying to ram through the reforms, and even working in concert with China.

Senior DPP lawmaker Wang Ting-yu told the chamber the legislation would illegally expand the power of lawmakers, including the power to punish companies and individuals who failed to comply with parliamentary inquiries.

"It gives lawmakers the power to punish people," he said. "Did people vote us in so that we can punish people?"

The KMT has 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 hindering parliament reform as it is afraid that there will be no place to hide malpractice and lies," it said in a statement.

Homemaker Mucha Kung brought her nine-year-old son to the protest.

"Are they becoming the Chinese Communist Party's spokespeople in Taiwan, trying to erode our democracy?" she said, referring to opposition politicians.

"China is threatening us with force and trying to sway our opinions with influence campaigns."

The protests were peaceful, with police maintaining a relatively light though obvious presence around parliament.

"I think China is the one that needs reform. Why do they have to meddle with us when they themselves do not have a democratic system?" said retiree Fong Jye-mei, 66.

Inside parliament, lawmakers chanted slogans and plastered the chamber with banners, occasionally scuffling, with debate going on late into the evening.

Last Friday, legislators threw punches during a debate on the reforms.

(Reporting by Fabian Hamacher, Anne Wang, Yimou Lee and Angie Teo; Writing by Ben Blanchard; Editing by Hugh Lawson)