The hard-fought Republican presidential campaign moved toward a new phase yesterday as Vice President Bush and Sen. Robert J. Dole (R-Kan.) prepared to take their bitter rivalry to a larger audience in the South and the second tier of candidates chose more precise targets.

In the wake of Bush's victory in New Hampshire, Dole expressed some regrets that he did not wage a more aggressive campaign there and vowed to fight Bush in the South.

Dole said his campaign "sat on our hands for three days" after his big Iowa triumph and "our expectations got out of hand."

"I'm not going to run from a fight," Dole said. But he indicated yesterday he may not attend Friday's Republican debate in Dallas, saying, "I'm not sure if I want to go to a Bush rally."

Dole's angry election-night charges that Bush had been lying about his record in television advertisements were echoed yesterday by his campaign manager, William Brock. "We're sick to the gills with this kind of cheap tactic," he said. "We don't have to wallow in the mud with them to answer their charges."

The calendar promises to keep the Bush-Dole contest alive in the weeks ahead. The next votes are to be cast in South Dakota Feb. 23, where Dole holds an edge, and in Minnesota caucuses, where Bush is leaving the field to others. Following his New Hampshire victory, Bush may now mount a serious fight in Maine, where delegates will be chosen Feb. 26-28.

While Dole stands to reap near-term victories, Bush is planning to campaign across the "Super Tuesday" states that vote March 8, and devote special attention to South Carolina, where the March 5 primary is considered a bellwether for the rest of the region. Bush advisers are also holding back on key strategy decisions until they see the results of new polls measuring his standing after the New Hampshire win.

As the two leading contenders laid plans yesterday for the southern contest, which is more oriented to media campaigning than the "retail" politics of Iowa and New Hampshire, the other Republicans were staking out less ambitious targets.

Rep. Jack Kemp (R-N.Y.), third in New Hampshire, has set his sights on Minnesota, where he campaigned yesterday, and South Carolina. Kemp, who must begin a new round of fund-raising to remain a viable candidate, is attempting to "score in a couple of places," according to his campaign manager, Charles Black.

Former television evangelist Pat Robertson declared yesterday that South Carolina would be "the big one for me," the state where he will prove he can win a primary election after succeeding only in caucus states suited to his high-intensity, well-organized evangelical Christian base of support.

"I'm throwing down the gauntlet to George Bush in South Carolina," Robertson told reporters in Greenville, S.C. When it was pointed out that he might be painting himself into a corner by saying "there's no question" he can win the state, Robertson replied, "I brought in my boats, landed the soldiers and burned the boats behind me."

Former Delaware governor Pierre S. (Pete) du Pont IV appears to be nearing the end of his presidential quest. Yesterday, a spokesman said du Pont, who finished fourth in New Hampshire, was still studying the options for a southern campaign. But du Pont has called a news conference in Wilmington today, and an informed source said he intends to announce his withdrawal from the race.

The shift to the South is certain to exacerbate the battle between Bush and Dole. Both candidates succeeded in "retail" campaigning in one state and now must adapt to the wider scope of a multistate primary. Bush rapidly switched to a more "grass-roots" approach only in the final days of the New Hampshire campaign.

Asked whether he intends to retain this approach in the South, Bush said, "I don't know. I think it helps a great deal to get the issues there in perspective. You've got a different problem -- 800 delegates at stake in one day." Campaign manager Lee Atwater said, "You move from a micro, parochial political situation into a very broad-based" campaign.

Bush campaign aides said they had considered and rejected the idea of pruning the large Bush organization after New Hampshire. Bush told cheering supporters here yesterday that "the system works" and praised their organizational efforts, promising to take "nothing for granted" in the South.

Meanwhile, strategists in both camps scrutinized the New Hampshire results. Tom Rath, former New Hampshire attorney general and a top Dole adviser in the state, said Bush's ties to Reagan proved too strong to overcome, even with Dole's Iowa triumph. "Ronald Reagan won this primary, not George Bush," he said. "We failed to sever the umbilical cord."

Bush advisers attributed the win to his aggressive new style, repeatedly attacking Dole in the final days of the campaign. The attacks included television advertising that accused Dole of waffling on the new arms-control treaty and an oil import fee. "You really had three days in which the vice president got out there and took the gloves off," Atwater said.

According to an ABC News exit poll, Bush clearly won the critical and hotly contested battle of the resumes. Government experience was the most important factor among Republicans in deciding which candidate to support. Of those who based their decision on the candidates' government experience, 55 percent voted for Bush, 37 percent for Dole.

Bush also benefited from voter perceptions of him as the candidate of the status quo. Only 3 percent of the vice president's supporters said they voted for him primarily because "he'd bring changes the country needs."

The exit poll results suggested that most New Hampshire Republicans want a president who will hew to the Reagan agenda. Three of four Republican voters agreed with the statement, "We need to keep the country moving in the direction Reagan has been taking us," although the fact that 25 percent want a change suggests some dissatisfaction in the president's party.

The exit poll showed Bush captured the largest share of those who want no fundamental change from Reagan. And nearly nine of 10 Bush partisans said they wanted a president who would continue Reagan policies, compared with three of five Dole voters.

Dole won nearly half of Republican voters who said the country needs a president "who can set the nation in a new direction."

While Bush ran strong among Republican Party faithful, Dole has far greater potential to attract Democratic crossover votes, according to the exit poll.

About half of all Democrats said they "definitely would not vote" for Bush, while only one of four made that statement about Dole.

The Iran-contra afffair hurt Bush in New Hampshire, although the damage was minimal. About one of eight Republican primary voters -- 13 percent -- said the scandal was a "very important" factor in determining their vote.

And of that group, more than two of three voted for a candidate other than the vice president, with Dole picking up 28 percent of this anti-Bush vote and Robertson getting 16 percent.

Staff writers T.R. Reid and Gwen Ifill, polling director Richard Morin and staff researcher Michelle Hall contributed to this report.