President Reagan repeated last night that he will choose Vice President Bush again as his running mate if he seeks reelection next year, but he stopped short of telling fellow Republicans that he will run for a second term.

"When I needed someone of unquestionable leadership, loyalty and skill, there is only one person I could--or would--choose again, and that's my partner and your vice president, George Bush," Reagan said at the annual Republican Senate and House campaign committees' fund-raising dinner.

The president predicted that Republicans "will celebrate a magnificent victory in 1984," a remark that some administration officials said could be interpreted as a broad hint that he will run. Reagan, however, has said he has not made up his mind, and no announcement is expected before Labor Day.

In brief remarks, Bush talked as if the president were already a candidate for reelection, and joked, about 1984: "Bet on the California entry--and I don't mean Alan Cranston," referring to the Democratic presidential candidate.

White House press secretary James S. Brady, severely wounded two years ago in the attempt on Reagan's life outside the Washington Hilton, shared the spotlight with the president at last night's dinner, held at the same hotel.

A check for $251,186--10 percent of the more than $2.5 million that the dinner raised--was donated to the James S. Brady Presidential Foundation, formed to assist needy individuals who are injured in an assassination attempt on a president or other high federal official.

Former secretary of defense Donald Rumsfeld, a longtime friend, and Hall of Fame Chicago Cubs baseball player Ernie Banks led a tribute to Brady and his wife, Sarah, who were greeted with an emotional standing ovation. The tribute included a taped song from country singer Willie Nelson that was played often during the 1980 campaign, and a taped message from Walter Cronkite that lauded the courage of the Bradys.

Reagan's remarks last night strongly defended his record, but he muted some of the partisan rhetoric customary at political events in what White House officials said was a deliberate attempt to preserve his "bipartisan" attempt to win congressional support for the MX missile.

When Reagan discussed the MX he referred to the support of "responsible Democrats and Republicans." But when he talked about economic issues his speech was peppered with phrases such as "Democratic tax increases."

As Reagan presented it last night, the White House and the Republican Party have worked together against Democratic opposition to promote economic recovery.

"Isn't it time for Republicans to stand shoulder to shoulder and tell our critics: 'If you won't work with us, if you can't cooperate and help to keep America moving forward, then stand aside, get out of the way and let us get on with it'?" Reagan asked.

The president made no mention of the opposition of prominent GOP senators to a number of his fiscal proposals, as demonstrated yesterday in the defeat of a compromise budget resolution.

As he has before, Reagan promised to veto any congressional action that would undo the third year of the tax cut or roll back tax indexing.

"Some of our opponents are only comfortable trusting government," Reagan said. "Their solutions would bring us back full circle to the source of our economic problems . . . .

"Our road is bold and filled with hope and opportunity. Their road is timid and relies on fear and envy."