Lawmakers backed the motion on Tuesday, which paves the way for a referendum that would allow Kagame (pictured left) to seek a third term in office.
Votes took place in both houses of the bicameral parliament, with both assemblies packed and holding parallel debates.
Both lawmakers and government supporters were present as the vote took place, with the president's name being chanted by spectators.
Kagame has not said he wished to stand for a third term, but he has said he is willing to listen to arguments that the two-term limit needs to be changed.
More than 3.7 million people - more than half the electorate - have signed a petition that calls for an amendment to Article 101 of the constitution, which limits the number of terms a president may seek to two.
"I want to thank all members of parliament for showing support to the people's wishes," parliament speaker Donatilla Mukabalisa said.
"There was a request that we engage the people and consult them about the amendment of 101, and other articles," Mukabalisa added. "I promise you we are going to fast track the process as requested."
Legal challenge against change
Rwanda's main opposition group, the Green Party, had complained that parliament should not hold the vote ahead of a court challenge against the referendum.
The situation had drawn parallels with neighboring Burundi, which had been left in political turmoil since April when President Pierre Nkurunziza announced bid to stand for a third term.
While Kagame's government has been credited with turning the country's economy around since the end of the Rwandan genocide in 1994, the president has been accused of authoritarian tendencies.
Kagame became president in 2000, although he had been the country's de facto leader even before then. His Rwandan Patriotic Front (RPF) rebels put an end to a genocide by Hutu extremists that left an estimated 800,000 people, mostly ethnic Tutsis, dead.
rc/jil (AFP, AP, dpa, Reuters)