Sixty-nine percent of Americans say race relations are generally bad, one of the highest levels of discord since the 1992 riots in Los Angeles during the Rodney King case, according to the latest New York Times/CBS News poll.

The poll, conducted from Friday, the day after the killing of five Dallas police officers, until Tuesday, found that six in 10 Americans say race relations were growing worse, up from 38 percent a year ago.

Racial discontent is at its highest point in the Obama presidency and at the same level as after the riots touched off by the 1992 acquittal of Los Angeles police officers charged in Mr. King’s beating.

Relations between black Americans and the police have become so brittle that more than half of black people say they were not surprised by the attack that killed five police officers and wounded nine others in Dallas last week. Nearly half of white Americans say that they, too, were unsurprised by the episode, the survey found.