WASHINGTON — Mayor Giuliani’s decision not to denounce the flying of the Confederate flag over Southern state capitols puts him at odds with Senator McCain on the flash-point issue, and it drew a sharp rebuke yesterday from his longtime New York nemesis, the Reverend Al Sharpton.

Asked by reporters in Montgomery, Ala., on Tuesday for his position on flying the Dixie flag, which many African-Americans say is a symbol of racism, Mr. Giuliani said it was a “good thing to be left on a state-by-state basis,” the Associated Press reported.

He made similar comments yesterday during a campaign stop in Georgia, where he also said the decision to apologize for slavery was a state issue, the AP reported.

Rev. Sharpton, who frequently criticized Mr. Giuliani on racial issues during his time as mayor, said it was “in line with positions that he would hold.”

“The whole idea of the Confederacy was a states’ rights issue, so he’s historically correct, which is why he and others should be denouncing it if they want to be president of the United States,” Rev. Sharpton told The New York Sun yesterday. “You can’t ask to be the head of the union but not take a firm stand against states’ rights that divide the union.”

The activist also took Mr. Giuliani to task for voicing support for the embattled talk show host Don Imus. While criticizing Mr. Imus’s remarks about the Rutgers University women’s basketball team, the former mayor said he would be willing to appear on his show again.

“It’s clear that Mr. Giuliani, in one week saying that about the flag in Alabama and reaffirms he’ll go on Don Imus, is clearly setting a tone that his campaign will not be one of inclusiveness,” Rev. Sharpton said.

Mr. Giuliani’s campaign declined to respond to Rev. Sharpton’s comments last night. Aides said his position on the Confederate flag has been consistent since 1998.

The issue is one of many politically thorny questions Mr. Giuliani has faced as he campaigns among conservatives in the South for the Republican presidential nomination. After a swing through Missouri and Iowa this weekend, he is scheduled to speak on Tuesday at a Christian school in Virginia Beach, Va., Regent University.

The issue has proved tricky, and potentially hazardous, for presidential candidates in recent elections. While black leaders have long railed against the display of the flag as offensive, many conservatives have said it is merely a symbol of Southern pride and should not be seen as racist.

Senator McCain of Arizona initially took the “states’ rights” position during his candidacy in 2000, but he later reversed course and opposed the flying of the flag. Then-Governor George W. Bush refused to denounce the Confederate flag and went on to defeat Mr. McCain in the key South Carolina primary.

In an appearance on “60 Minutes” this week, Mr. McCain said he earlier called it a state issue “clearly knowing it wasn’t.” He said he took that position then out of “ambition” and called the Confederate flag “a very offensive symbol to many, many Americans.”

A former Massachusetts governor, Mitt Romney, has rarely faced the flag question on the campaign trail so far, but a campaign spokesman confirmed yesterday that Mr. Romney believes it is a state issue.

The issue has caused trouble in Democratic politics, as well. In the 2004 election, Howard Dean drew heavy criticism from his primary opponents for saying he wanted to be the candidate “for guys with Confederate flags in their pickup trucks.” He later backed off the comment, saying he wanted “people with Confederate flags in their pickup trucks to put down those flags and vote Democratic.”

A civil rights group, the Southern Poverty Law Center, disputed the contention that the flags were displayed on or near state capitols to evoke Southern pride or that they originated there in the early 1960s to mark the anniversary of the beginning of the Civil War.

“These flags were not raised to represent some kind of pride in Southern life or some nostalgic anniversary,” a spokesman, Mark Potok, said. “They were raised as a direct rejection of attempts to desegregate Southern schools. They were raised as part of a racist wave.”

A Texas-based researcher who has written extensively on the neo-Confederate movement, Edward Sebesta, said Mr. Giuliani’s comments appeared evasive. “I think he can’t face the issue,” Mr. Sebesta, who called the flag a symbol of “white supremacy,” said, “He can’t say yes or no.”