The Democratic Party says chief executive-elect Leung Chun-ying lied during the election campaign when he claimed he had no illegal structures at his home on The Peak.
The party wants to file an election petition, which challenges an election result, or a judicial review, which asks a court to review a government action - or both.
Last week, the public found out that Leung had six illegal structures at his HK$500 million property at No 4 Peel Rise. They include an illegal cover on a parking space, a 40 sq ft storage room, and a 240 sq ft basement.
Democrat chairman Albert Ho Chun-yan says Leung has ruined his good name. This was especially bad because he had pointed a finger at fellow candidate Henry Tang Ying-yen during a public debate, accusing Tang of having a huge illegal structure in his home, Ho added.
The law says that Ho should have filed a petition within seven working days or a review within 30 days after the result was declared on March 25. But he said the court could decide to accept late requests, especially with a judicial review.
Meanwhile, workers spent nine hours yesterday taking down two of the structures.
The media used at least six cranes to watch the work.
Leung said sorry again yesterday, and that he never meant to cover up the illegal structures at his home.
Leung said he was disappointed that he had let his supporters down, but that he had not known the structures were illegal when he had bought the home.
The Democrats, Civic Party and Labour Party said they wanted a special question-and-answer session before July 18, but the Democratic Alliance for the Betterment and Progress of Hong Kong questioned the need.