SEOUL, South Korea — President Park Geun-hye appeared on Wednesday to have stalled a bid to impeach her in South Korea’s National Assembly, at least temporarily, as lawmakers debated how to respond to her surprise offer to resign.

South Korea’s three opposition parties vowed to continue their push to impeach Ms. Park, whose government has been crippled by a corruption scandal. But her speech on Tuesday appeared to have swayed some lawmakers in her party who had favored impeachment but now say they are willing to let her step down voluntarily as late as April. Complicating the matter further, some lawmakers said rewriting the country’s Constitution would be the best way to end her term in office.

Opposition politicians expressed fury over Ms. Park’s five-minute address to the nation, in which she said she was willing to leave office before the end of her term but left the details — including the date — to the National Assembly, which has a reputation for being able to agree on very little. They called it a ploy meant to derail the impeachment bid, which before Tuesday had appeared within reach of gaining enough support in Ms. Park’s party for a vote as early as Friday.

“Her offer is like that of a student who faces expulsion for breaking school regulations but demands an early graduation,” Sim Sang-jung, an opposition leader, said on Wednesday in a widely shared Twitter post.