Senator Barack Obama is poised to reach a milestone in the presidential race on Tuesday by capturing a majority of pledged delegates, but he said he would not declare victory against Senator Hillary Rodham Clinton or suggest the Democratic primary should end until the final three contests are finished on June 3.

For Mr. Obama, the situation is delicate. While eager to proceed to a general election match with Senator John McCain of Arizona, the likely Republican nominee, Mr. Obama is also trying to bring the contest to a close in a way that allows him to win over Mrs. Clinton’s supporters and unify the party.

For her part, Mrs. Clinton is making a counterargument that she is winning the popular vote if Florida and Michigan are counted, and that the party’s leaders should take that into consideration before deciding which candidate to support.

The results from the Kentucky and Oregon primaries on Tuesday will almost certainly allow Mr. Obama to reach a threshold that his campaign has long sought to establish as the critical measure of the will of the party: winning a majority of the delegates awarded in primaries and caucuses. He also continues to gather support from the party leaders known as superdelegates that he still needs to secure the nomination, picking up five more endorsements on Monday.