Legislators on Friday voted 93 to 17 to back a proposal to debate Kuczynski’s dismissal on December 21.
The president’s impeachment would need 87 votes in the 130-strong Congress.
Kuczynski, who is expected to appear before Congress before the final vote, is accused of covering up decades-old illegal payments from Brazilian construction giant Odebrecht.
The company became embroiled in a political scandal after admitting to paying more than $788m in bribes to win construction contracts across 12 countries, including Argentina, Mexico and Venezuela.
The multiparty motion said Kuczynski lacks the “moral capacity” to govern, and accused the president of lying to Peruvians about his relationship with Odebrecht.
Kuczynski has refused calls to stand down, and denies receiving illegal payments, saying he provided advisory services to the company.
“I’m not running and I’m not hiding because I have no reason to,” Kuczynski said in a televised speech on Thursday.
The accusations centre on Westfield Capital Ltd, a company owned by Kuczynski, which received $782,000 from Odebrecht, according to Peruvian national paper El Comercio.
Kuczynski, a former World Bank official, denies having a managerial role in his company and has promised to produce his financial records.
Marcelo Odebrecht, the former company president of Odebrecht, is currently serving a 19-year jail sentence in Brazil.
Kuczynski is the latest Latin American politician to be linked to the scandal, which saw Ecuadorian Vice President Jorge Glas sentenced to six years in prison on Wednesday, for taking $13.5m in bribes from Odebrecht.