Sen. Robert J. Dole (R-Kan.) yesterday questioned Vice President Bush's competence in dealing with the Iran-contra scandal and suggested that Bush's low level of support among independent and Democratic voters would make him a weak Republican nominee for president.

"When your strength is foreign policy, you could ask questions," Dole told a group of reporters. The remark was an apparent reference to Bush's claim that his role in the administration decision to sell arms to Iran should not be criticized because he had been "denied information."

Dole said he had no intention of picking a "quarrel" with Bush. But he noted that in seeking the support of an unidentified Republican National Committee official, he stressed his own relatively high favorability ratings among independents and Democrats, in contrast to lower ratings for Bush.

The national committeeman "wants a qualified winner, not a qualified loser," Dole said. "I think there's evidence that I at least now elicit a better response from independents and Democrats than any other Republican candidate."

Dole said that while campaigning he has run into questioners who want to be sure that, if elected president, "I'm not going to have people who keep secrets from me because they think it's in the best interests of the country . . . . I think competence is going to be on the minds of some people . . . . I think toughness is going to be a factor."

Without mentioning Bush, Dole's remarks appeared to be aimed at pointing up the role Bush played in the administration's handling of the sale of arms to Iran.

In a recent interview with The Washington Post, Bush said he had no idea there had been a "raging fight" taking place within the administration over arms sales. "I didn't attend the meeting where that was brought up. I was off at the Army-Navy football game," he said. "We were not in the loop."

Dole held the session with reporters in part to promote his extensive campaign activities during the August congressional recess -- during which he plans to go to 28 states -- and to argue that he has put together strong organizations in key primary and caucus states.

"I do believe that there are only two of us with broad-based organizations . . . who have established we have the organizations and can raise the money," Dole said, referring to himself and Bush. During his 1980 presidential bid, Dole was criticized for failing to build strong organizational structures.

At the session, Dole and campaign aides disavowed a statement by the deputy chairman of his Iowa campaign, Steve Roberts, who told the Des Moines Register, "If Dole doesn't do well in Iowa, he is through, and I would say the presidential race is through on the Republican side." Dole said there is "going to be a lot of pressure on George Bush {in Iowa}, more than on Bob Dole."

The Senate minority leader said he intends to use his support of Supreme Court nominee Robert H. Bork on the campaign trail. And in a later speech on the Senate floor, Dole warned that "the American people will not tolerate a filibuster" against the Bork nomination that would leave "the court short-handed and justice ill-served."Staff writer Edward Walsh contributed to this report.