The source says Burris has begun informing Democratic officials about his decision.
Burris was appointed by disgraced Illinois Gov. Rod Blagojevich to fill the Senate seat vacated by President Barack Obama. His appointment was criticized from the moment it was announced and prompted calls for Burris to resign.
In the Senate, Burris has been treated as something of a pariah because of his ties to Blagojevich, who was arrested in part on allegations he tried to sell the Senate seat.
By not running for re-election, Burris increases Democrats chances of holding on to the Senate seat in 2010. Republicans had viewed Burris as a potentially easy target if he were to run for a full-term in the Senate.
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