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Erie County Legislator Barbara Miller-Williams said Thursday she will not enter the Democratic primary for the State Senate seat now held by Timothy M. Kennedy.

“I have a lot of respect for Sen. Tim Kennedy and I certainly do not want to run against him,” she said. “I simply don’t have an interest at this time.”

Miller-Williams did not entirely close the door on a Senate candidacy this year, acknowledging that some Democrats continue to urge her to run. But she also said she does not anticipate changing her mind.

Kennedy is already facing a primary challenge from Legislator Betty Jean Grant, and some observers say the incumbent would benefit by facing two black opponents who might be expected to diffuse the African-American vote in the district.

A source close to the situation said efforts are still underway, however, to entice another African-American Democrat into the primary race.