Democrat Michael Dukakis, more direct each day in his claim to the party's presidential nomination, arrived in California with plain assurances to Jesse Jackson supporters that his rival would be considered as a running mate.

"He has done a remarkable job," the Massachusetts governor declared before leaving his state to campaign in California through next week's season-ending primary. "I don't think that gives you a leg up, and he himself has said that it's up to the nominee to pick his running mate and I agree with him."(But) I think any of the people who went out and worked hard, ran for the presidency and demonstrated the ability to put a campaign together and win votes, have earned that right to be considered. Because he has done so, of course, he's somebody who should be considered."

Dukakis used a predominantly black community college in Boston's Roxbury neighborhood as his backdrop Wednesday to increase the courtship of Jackson and the voting bloc seen as vital to Democratic White House dreams.

The three-term governor pledged to convince blacks and other minorities that the answer to their concerns lies in a Democratic president, even if it is not the civil rights leader they favor.

For his part, Jackson repeated his claim to have "earned consideration" as the vice presidential nominee - although he told an audience in New Jersey before flying to California, "I have not yet made a judgment about whether I will pursue that nomination or not."

His most significant achievement, he argues, is the application of pressure on Dukakis and the apparent Republican nominee, Vice President George Bush, to take some of his most cherished issues - such as the war against drugs - to the top of the nation's political agenda.

Wednesday night Jackson delivered a tough anti-drug message to about 1,000 people in the rough Watts area of Los Angeles, twice plunging into the crowd to shake hands and to talk with people.

Jackson was scheduled to meet later Thursday with members of youth gangs from the area.

He arranged to spend Wednesday night in the tough Nickerson Gardens housing project and said he would meet with gang leaders this morning.

Jackson warned the neighborhood rife with gang warfare over lucrative cocaine turf: "When I become president, you drug-pushing, gun-carrying bullies are going to catch hell from Washington! . . . Nobody has earned the right to sell drugs to their neighbor. Nobody has earned the right to kill their neighbor."

The grim atmosphere stood in marked contrast to the Hollywood fund-raiser the candidate attended earlier Wednesday evening with hosts Kris Kristofferson, Rita Coolidge and Natalie Cole. Jackson was scheduled Thursday to debate Dukakis in more moderate surroundings in the Los Angeles suburb of Torrance.

In related developments:

-The Washington Times reported Thursday that Jackson campaign aides have been trying to arrange a tour of foreign troublespots to keep his profile high until the convention in Atlanta July 18-21. Early focus was on Vietnam, the newspaper said, but the more likely itinerary is Central America and Africa.

-Dukakis administration officials increased their estimate of Massachusetts' growing shortfall in tax revenues from $250 million to $300 million, the third upward revision in recent months. Democrats blame the problem on the 1986 federal tax reform law, but Republicans accuse the governor of overspending.

-Dukakis was endorsed by Rep. Claude Pepper, D-Fla., in a May 27 letter made public Wednesday. Pepper, at 87 the oldest member of Congress and a champion of America's senior citizens, formerly supported and appeared in advertising for Rep. Richard Gephardt, D-Mo., who dropped out of the race in March.