Ninety-three of the 118 legislators present yesterday supported the proposal to debate impeachment on December 21.
"This decision will be communicated to the president to exercise his right to defence (during the next session) and assist with a lawyer if required," said Luis Galarreta, the head of Peru's single-chamber Congress.
Dismissal of Kuczynski would require support from 87 of the chamber's 130 members.
The rightwing Popular Force party, which controls the legislature, had already warned it would begin impeachment proceedings if the president did not resign by next Thursday.
More From This Section
"I am not going to abdicate my honour, my values or my responsibilities as president," Kuczynski said in a televised speech to the nation late on Thursday, backed by his ministers.
"I won't run, I won't hide nor do I have any reason to do so," he said, promising to cooperate with investigations by Congress and the office of the attorney general.
On Wednesday, Odebrecht said it had paid Kuczynski USD 5 million in consulting fees between 2004 and 2013.
For part of that period, Kuczynski was economy minister and head of cabinet for then-president Alejandro Toledo, whom Odebrecht paid USD 20 million in kickbacks to win a contract managing a highway project, the company said.
He is the third Peruvian president to become embroiled in the Odebrecht affair.
Former president Ollanta Humala is in preventive detention, accused of receiving USD 3 million from Odebrecht to fund his political campaigns, while Toledo faces an order for his extradition from the United States.
The Odebrecht scandal has ensnared politicians in several other countries including Ecuador, Mexico, Panama and Venezuela.
Under investigation by the US Justice Department, Odebrecht agreed in December 2016 to pay a record USD 3.5 billion fine after admitting to paying USD 788 million in bribes across 12 countries to secure contracts.