The ruling Rwanda Patriotic Front (RPF) approved the bid even though the country's constitution provides for two presidential term limits.
RPF issued a statement on Monday backing a constitutional change after about 600 high-ranking members held a two-day retreat in the capital Kigali.
"Based on the wishes of Rwandans and party members that have been recently expressed, we support that the [constitution]... should be amended," the RPF statement read.
Kagame is coming to the end of his second seven-year term and has argued that the constitution had been drawn up by the people and they can determine any changes to the charter.
Instead of an opposition, over 3.6 million people signed a petition urging parliament to change the constitution to allow Kagame to run.
In early April, he said he disagreed with initiatives to amend the constitution but was "open" to being convinced otherwise.
However, observers say most of the people who signed the petition did so under duress.
Kagame has since addressed the claims.
"If the allegations that some people have been forced are true, that's a concern and you should also have that concern," Kagame told RPF members.
Kagame's criicis say he tramples on media and political freedoms, and does not deserve a third term.
But supporters argue Rwanda has made significant progress since the 1994 genocide and Kagame would transform the country into a middle-income country by 2020.
While Rwanda has remained relatively peaceful under Kagame's leadership and the RPF's plan for a third term, neighbouring Burundi under similar circumstances has declined into civic unrest.
Burundi President Pierre Nkurunziza expressed interest in a third term bid on April 25 and the announcement triggered weeks of violent protests by opponents who said the move violated the constitution.
But analysts do not anticipate a similar eruption in Rwanda if Kagame runs again.
Source: Theafricareport.com
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