Kagame, 57, has been at the helm of Rwandan politics since 1994, when an offensive by his Rwandan Patriotic Front (RPF) rebels put an end to a genocide by Hutu extremists that left an estimated 800,000 people dead, most of whom were Tutsis.
He was initially welcomed by the West but there have been growing concerns about his strongman rule -- critics say that he has silenced the opposition and the media.
He added, "President Kagame has repeatedly stated his commitment to respecting constitutional term limits and to mentoring a generation of leaders able to sustain Rwanda's remarkable economic growth and stability.
"The United States underscores the importance of these commitments."
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Rwandan lawmakers recently said they found only 10 people in nationwide consultations who opposed possible constitutional changes to allow Kagame a third term.
Any change to the constitution would require a vote in support of at least three-quarters of both houses of parliament, followed by a national referendum. Lawmakers had voted in July in initial support of the idea of a change.
He was re-elected in 2010 with a similarly resounding mandate. The next elections are due in 2017.
Kagame says the decision on a third term is for the "Rwandan people.