Bush Advisers Divided Over Whether to Uncork Knock-Out Punch at Rival Perot : Republicans: Some think challenger is on the ropes, should be finished off. So far, the prevailing view urges caution.

After a week of doing their best to batter rival Ross Perot, political advisers to President Bush have begun a high-stakes debate over whether to maintain the barrage. With a swagger reflecting their hope that the coordinated attack has left Perot wounded, the Bush advisers likened their dilemma to that of a boxer who has backed his opponent against the ropes but is wary of leaving himself exposed to a counterpunch.

Some Bush advisers, including Republican National Committee Chairman Richard N. Bond, are said to believe that allegations that Perot privately investigated his employees, competitors and Bush himself have presented the White House an opportunity to all but knock Perot out of the race.

But top officials at Bush’s reelection headquarters have warned that continued attempts by Republicans to compound the Texas billionaire’s troubles could give Perot a new opportunity to blame the White House for alleged dirty tricks.

“I think that with Perot we shouldn’t even enter the fray,” said Robert A. Mosbacher, the general chairman of Bush’s reelection campaign. “I just don’t think this is something we should get into.”

Mosbacher acknowledged that his view had been challenged by “a few” other senior Bush advisers. But Bush was said to have urged a similar caution during a White House strategy session on Tuesday, and Mosbacher said bluntly: “The one who matters is with me.”

The debate over tactics comes after a week of furious exchanges between the Bush and Perot camps.

Bush Administration officials jumped on press reports that Perot had once investigated a land deal involving a former Bush business partner, and had looked into some dealings by Bush’s children.

Perot denied that he had investigated Bush’s children. He said he had been curious about the tax implications of the land deal, and had turned over the information to the Washington Post when asked. He charged that the Republican campaign was orchestrating an effort to discredit him.

Advisers to both Bush and Perot suggested the battle could mark a turning point in the campaign. “We either take Bush out or he takes us out,” Edward J. Rollins, co-manager of the Perot petition committee, told the Washington Post. “And it’s (likely to be decided) this summer.”

Bush aides said a final decision on how hard to press their attacks on Perot would not be made until next week. But they said Republicans would in the interim almost certainly begin to mute their attacks in the hope that continued disclosure about Perot would by itself exact sufficient damage.

“Do you keep things perking or do you back off a little bit and let him stew in his own words?” one senior Bush adviser said in posing the dilemma for the campaign. “Right now, the best thing we can do is let actions take their course.”

“We’re in danger of crossing the line,” another Bush aide warned. During the last week, Bush suggested that Perot’s reported interest in allegations about his son’s business activities in 1986 was “not particularly American,” Bond appeared on three network television shows in the space of 12 hours to raise doubt about Perot’s character and even Budget Director Richard G. Darman and drug czar Bob Martinez joined in the anti-Perot campaign. “Another couple of steps, and we’d be proving Perot’s argument for him,” the aide said.

The most important voice urging restraint from the Bush camp was said to have been that of the President himself, who wondered aloud during a White House strategy session Tuesday whether his advisers really needed to speak out so critically of Perot.

Republican officials said Bond believes such an attack strategy can only help Bush, and that view was endorsed by another senior White House adviser in an interview Thursday. But in interviews Friday, several Bush aides acknowledged misgivings about maintaining a concerted effort to portray their rival as “scary” or otherwise unpalatable.

For one thing, the officials said such a course could be a big help to presumptive Democratic candidate Bill Clinton.

“We want to keep our foot on Clinton’s throat,” one senior Bush aide said.

In addition, a Republican source close to the White House said the campaign had been motivated in part by a “nightmare scenario” that a too-often tormented Perot might eventually throw his support--and his wallet--to Clinton.

Aides said Mosbacher, Bush campaign chairman Robert M. Teeter and others began to have second thoughts about attacking Perot when Perot responded sharply to Bush’s “not particularly American” remark. Perot said that he had simply turned over to Bush information that had come to his attention, and revealed that the then-vice president had written him an effusive letter of thanks for what Bush characterized as a gesture of concern for his son.

“That might have been a bit of a bad bounce,” a senior campaign official said of the incident. But even while turning cautious, Mosbacher and others within the campaign insisted that efforts by newspapers and others to probe the Perot record would continue to cause trouble for their rival’s campaign.

Among Perot’s advisers, there is said to be some difference of opinion over whether to continue responding to the GOP attacks and over just how critical the next several weeks are to Perot’s presidential bid.

The candidate himself seemed to reflect that divergence of views.

In Hartford, Conn., on Thursday morning, Perot emerged in a combative mood from a private reception with volunteers. He continued to trade long-distance barbs with the President’s surrogates.

But just hours later, speaking to several thousand volunteers at the city’s Bushnell Park during a noon rally, Perot vowed to “get back to the basics,” urging backers not be “distracted” by the GOP attacks on him.

Times staff writer Edwin Chen contributed to this article.