Burris also is refusing to say whether he'll run for the seat in 2010.
Burris was appointed by disgraced former Gov. Rod Blagojevich, who was impeached and driven from office after he was accused of trying to sell the Senate seat vacated by President Barack Obama.
Burris repeatedly changed his story about how he was appointed.
He is facing calls for his resignation after he admitted trying to raise money for Blagojevich. Burris has said he did nothing improper. He refused to comment after his meeting with Durbin.
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