Michael Dukakis was finding some relief from a politically embarrassing budget crisis in his home state as Vice President George Bush pledged to right "a wrong that has been out there for many years" and appoint a Hispanic American to his Cabinet.

Dukakis, the Massachusetts governor, was spending most of Thursday in his Statehouse office before heading west for three days of campaigning. He was preparing to review a proposed fiscal 1989 state budget compromise.Massachusetts House and Senate leaders agreed late Wednesday on a compromise budget of $11.75 billion that would increase state spending about 4 percent.

Dukakis was forced to seek emergency spending authority this week to keep government functioning. Massachusetts faces a $450 million deficit on an $11 billion budget in the just-ended fiscal year.

Dukakis has been highly critical of the Reagan administration's deficit spending, and Republicans are planning to make political hay of his troubles.

"It could turn out to be the Achilles heel of the Dukakis presidential campaign," said state Sen. Paul Cellucci, a Massachusetts coordinator for the Bush campaign.

Dukakis, for his part, continued to attack the ethical standards of the Reagan administration, saying the resignation of Attorney General Edwin Meese III does not erase the administration's shoddy record.

"If someone in my administration is caught breaking the law, we won't make excuses for him, we'll prosecute him," he told a friendly audience of Greek-Americans in Boston.

Bush was traveling to Boston tonight to address the same ethnic group at a Greek Orthodox diocesan dinner. Aides said Bush was going to talk about the importance of religion.

Dukakis was traveling to Dallas Thursday night to address a convention of the League of United Latin American Citizens, the same group to whom Bush promised Wednesday he would make a Hispanic appointment.

Bush said after addressing LULAC, the largest and oldest Hispanic American civic group, that he would not go around the country making the same promise to other special interest groups.

"Other groups have been represented in the Cabinet and Hispanics have not," said Bush.

"I will be very open-minded and broad-based in who I select to serve in my Cabinet, but I'm addressing myself to righting a wrong that has been out there for many years," he said.

Oscar Moran, the group's president, said Bush "attracted the attention of some voters who already decided on Dukakis."

But Tony Bonilla, an influential Democrat in the group, said it was "a little patronizing" for Bush to make such a statement after serving eight years in the Reagan administration without a Hispanic in the inner circle.

Hispanics are a politically important group, especially in key battleground states like Texas, California and Florida. Dukakis' command of Spanish gives him an advantage in competing for votes from those groups.

Dukakis met for more than an hour Wednesday with 20 national civil rights leaders, including NAACP executive director Benjamin Hooks, National Urban League President John Jacob, the Rev. Joseph Lowery of the Southern Christian Leadership Conference and Coretta Scott King, the widow of Martin Luther King Jr.

"I cannot recall an issue he disagreed with us on," Hooks said. But whether blacks will support Dukakis without Jesse Jackson on the ticket is largely up to Jackson, Hooks said.

Jackson, meanwhile, met with Arab leaders at the United Nations. Afterward he emphasized that the shooting down of an Iranian passenger jet by a U.S. ship in the Persian Gulf was "an accident, an error."

Jackson called for a period of mourning for the attack victims.