Tensions are high in the semi-autonomous city as fears grow that Beijing is tightening its grip, fuelling an independence movement in Hong Kong.
The former British colony was handed back to China in 1997 under an agreement protecting its freedoms for 50 years, but there are concerns those liberties are being eroded.
A new wave of lawmakers advocating independence and self-determination were voted into the Legislative Council (Legco) -- Hong Kong's lawmaking body -- in citywide polls last month.
The oath states that Hong Kong is a special administrative region of China.
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Both refused to pronounce China properly, and Yau was heard to replace the words "the People's Republic of China" with "the People's refucking of Zeena".
They were given permission to retake their oaths on Wednesday, but when it came time to do so, pro-Beijing lawmakers walked out, forcing the meeting to be suspended due to an insufficient number of legislators in the chamber.
"If they want people to respect their oaths, they have to express regret over their behaviour last week and to apologise to all Chinese around the world," pro-Beijing lawmaker Priscilla Leung told reporters.
Her fellow legislators chanted "Apologise!"
Hundreds of pro-Beijing supporters waved Chinese flags and stamped on pictures of Baggio and Yau outside the legislative council building ahead of the swearing in.
Baggio and Yau said they wanted to complete their oaths, but would not apologise for last week's behaviour.
"We are empowered by the people to enter the Legco," Baggio said.
The session was eventually adjourned without Yau and Baggio having the chance to make their pledges.
The chaotic scenes came after a late-night court bid on Tuesday by city leader Leung Chun-ying and justice secretary Rimsky Yuen to block the pair from taking up their seats.