Michael Dukakis, harvesting another pair of landslide primary victories, sounded ever more confident of his claim to the Democratic presidential nomination while Republican George Bush looked ahead to the fall and cautioned his supporters, "We've got a long way to go."

Jesse Jackson scored an expected victory Tuesday in the District of Columbia but found himself slipping another 120 delegates behind Dukakis, who won handily in Ohio and Indiana.His latest victories moved Dukakis to fewer than 600 delegates from the 2,081 he needed to clinch the nomination. He also moved more than 600 ahead of his only rival.

But Jackson gave no sign he was ready to end what he called a struggle "for the direction of our party and the soul of our nation."

"All the way to California and New Jersey!" he said, referring to the two biggest states holding primaries on June 7.

Jackson was seeking support Wednesday among House Democrats and then holding strategy sessions with aides before flying off to Nebraska, which holds its primary next Tuesday, as does West Virginia.

Democratic Party leaders tempered their euphoria over the latest signal that their nomination marathon was over with concern that Jackson's recent attacks on Dukakis could provide campaign ammunition for the Republicans in the fall.

"I would hope he wouldn't say anything that could be used against Mike in the general election," said Gov. Bill Clinton of Arkansas, who predicted Dukakis would win the Democratic nomination on the first ballot at the party convention in July.

Judy Carnahan, chairman of the Oregon Democratic Party, said Jackson's recent attacks were "very disappointing. What he's managing to do is diminish his own stature."

That view was by no means unanimous.

Lynn Cutler, vice chair of the Democratic National Committee, said she wasn't concerned about Jackson's rhetoric.

"I don't think any of it is stuff we're going to see coming back at us out of George Bush's mouth," she said. "He's trying to draw distinctions, and I don't blame him for that. I don't think there is anything there that is problematic."

When Dukakis was asked if he thought Jackson should tone down his attacks, the Massachusetts governor replied, "He's got to make that judgment. I'm going to try to keep this as positive as I can."