Burris was appointed by disgraced former Illinois Gov. Rod Blagojevich, who was impeached and driven from office after he was accused of trying to sell the Senate seat.
The committee's "Public Letter of Qualified Admonition" told Burris that while it found no violations of law, "Senators must meet a much higher standard of conduct."
The committee wrote Burris that his phone conversation with the former governor's brother was inappropriate. It says Robert Blagojevich called Burris on Nov. 13, 2008, seeking to raise funds for his brother, and Burris appeared to agree to write a check while also bringing up his desire to seek the Senate seat.
Burris is not running for a full term.