Pro-government Rwandan newspaper The New Times says hundreds of people turned up at parliament on Tuesday morning to watch the debate on presidential term limits.
Those who want Mr Kagame to stay credit him with “leading the struggle to stop the 1994 genocide”, it says.
On Monday, a ruling party RPF message was circulated on social media in the capital, Kigali, urging people to take buses to parliament to support Mr Kagame.
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The small opposition Green Party has been the only dissenting voice calling for the constitution not to be altered to allow for a third term, and petitioning instead for a single presidential term to be changed from seven to four years.
Last month, it went to the Supreme Court to try and stop the move to change the constitution, but the party was unable to get legal representation
The party has been given until 29 July to find a lawyer to take on the case.
In neighbouring Burundi, there have been violence clashes following a decision by President Pierre Nkurunziza to seek in a third term in elections next week.
The RPF’s rebel movement took power in Rwanda after the genocide in which some 800,000 ethnic Tutsis and moderate Hutus were killed.
President Kagame, who has won two elections, has been hailed by his supporters for driving rapid economic growth.