WASHINGTON — WASHINGTON -- President Bush walked a fine line yesterday between joining national outrage over the acquittal of four police officers in the Los Angeles beating case and finding greater fault with the rioters who took out their frustration through lethal violence. It was a balancing act that reflects competing demands on the president from his conservative political base and leaders of the black community who say he is insensitive to police brutality. "We tried to be equal . . . but eight people are dead," the White House spokesman, Marlin Fitzwater, said before the death toll had climbed higher. "That's certainly a matter that justifies anger." The balance may be even more difficult to maintain if the $H violence continues to spread, as it did yesterday to Atlanta and San Jose. "Politically, he can't offer any sympathy to those who are rioting," said one Bush adviser. "There's a difference between excusing and saying you understand the frustration." Mr. Bush refused to comment directly on the verdict in the Rodney King case, leaving aides to explain that the president wouldn't attempt to second-guess a jury when he hadn't heard all the evidence. In one of several statements on the topic, the president said, however, that he shared the "deep sense of personal frustration and anguish" felt by other Americans who had seen the videotape of the police officers beating Mr. King and found the acquittal hard to understand. Mr. Bush also made clear yesterday that the federal government is exploring other means to bring the police officers to justice. In impromptu comments Wednesday night, he had suggested those unhappy with the verdict should wait through the "appeals process." There is no appeal of an acquittal in a criminal case. However, the president's harshest language of the day was directed at the hundreds of rioters who set Los Angeles ablaze with its worst violence since the 1960s. "The murder and destruction in the streets of Los Angeles . . . must be stopped," Mr. Bush said during a brief White House appearance at noon, after which he refused to take questions. "Lootings, beatings, and random violence against innocent victims must be condemned. And society cannot tolerate this kind of behavior." While it seemed unlikely that the president's handling of the King verdict would have political implications for his re-election campaign, a senior Bush aide said the president might actually benefit from an outbreak of national violence. It would give him an opportunity to demonstrate his leadership ability, the aide said. In each of his statements yesterday, Mr. Bush stressed the importance of respect for the legal system and the imperative for law and order. He was supported in that stand by Patrick J. Buchanan, the conservative commentator who is challenging Mr. Bush in the Republican primaries and who appeared to be pushing him to take a harder line against the violence in Los Angeles. "It is the responsibility of the president of the United States to condemn that," he said. "No matter the anger over the verdict in the Rodney King case, it was decided in a fair trial by a conscientious jury." But Baltimore Mayor Kurt L. Schmoke was among those who criticized Mr. Bush for failing to bring action sooner against the police officers through the federal courts. "I just listened to the president, but I can say that for millions of Americans the reaction is going to be: 'It's not what you say, Mr. President, it's what you do'," Mr. Schmoke told the Associated Press. The Rev. Jesse L. Jackson, the civil rights leader, who met with Attorney General William P. Barr yesterday morning to urge speedy federal action, recalled that three days after the tape of the King beating appeared on television screens across the nation, Mr. Bush honored Los Angeles Police Chief Daryl F. Gates in a Rose Garden ceremony. "This sort of insensitivity undermines credibility in the judicial process," Mr. Jackson said yesterday. Chief Gates, who is scheduled to leave his post shortly as a result of ill-feeling created by the King case, was also embraced during the 1988 presidential campaign by Mr. Bush, who cast himself as a tough law-and-order candidate and pilloried his Democratic opponent, Michael S. Dukakis, for supposedly being weak on crime. Mr. Bush's Democratic opponents in this year's campaign went further than the president in criticizing the verdict. Arkansas Gov. Bill Clinton said he was "very disturbed" by the HTC acquittal and charged that Mr. Bush was partly to blame for the violence in Los Angeles by neglecting the racial and economic divisions in the country. "There is this deeper, larger problem of the feeling of neglect and abandonment that millions of Americans have and has now broken into the open in Los Angeles," Mr. Clinton said during a campaign stop in Chapel Hill, N.C. The president later fired back: "Yes, in some places in America, there is regrettably a cycle of poverty and despair. But if the system perpetuates this cycle, then we've got to change the system. We simply cannot condone violence as a way of changing the system." Former California Gov. Jerry Brown called it "an outrage that our system can't punish those, particularly police officers, who use the power and majesty of the state to beat some man senseless." He immediately re-routed his campaign from Nebraska to Los Angeles to try to "cool down the emotions" in the riot-torn area. Mr. Bush delayed for an hour or so a half-day campaign trip to Columbus, Ohio, so he could confer with Attorney General Barr and other top officials to discuss his response to the Los Angeles riots. During that meeting, he called Los Angeles Mayor Tom Bradley and California Gov. Pete Wilson to get their reading on the situation. The president is expected to meet today with a group of national black leaders assembled by Health Secretary Louis W. Sullivan, the only black member of the Bush Cabinet.