SEOUL, South Korea — South Korea’s three opposition parties said Friday that they would vote Dec. 9 on a motion to impeach President Park Geun-hye over the corruption scandal that has paralyzed her administration.

Ms. Park’s party hopes she will agree to resign by April instead, arguing that impeachment would then be unnecessary. The outcome of the political crisis is likely to depend on whether the rival camps can work out a compromise in the next week.

Some 172 opposition and independent lawmakers in the National Assembly have said they favor impeachment, not enough to meet the needed two-thirds threshold in the 300-seat body. Dozens of lawmakers from the president’s party had earlier said they would join that camp, but many of them changed their minds after Ms. Park said on Tuesday that she was willing to resign, while leaving the details — including the date — to the National Assembly.