The poll shows Obama, a U.S. senator from Illinois, leading U.S. Sen. Hillary Clinton, of New York, 40 percent to 35 percent in the Democratic primary. Former U.S. Sen. John Edwards, of North Carolina, who has dropped out of the race, was a distant third at 9 percent.

Obama's support among black voters grew from the poll three weeks ago when he had 54 percent of the black vote.

The poll that ended Tuesday gave Obama 68 percent of the black vote, while Clinton's black vote dropped from 20 percent Jan. 8 to 16 percent.

Among white Democrats, Clinton's white vote grew from 47 percent three weeks ago to 51 percent. Obama's white vote has stayed at about 17 percent.

The undecided Democratic vote is 16 percent and the margin of error, based on a sample of 373 voters, is plus or minus 5 percentage points, meaning Obama and Clinton could be tied.