The former Republican presidential candidate Mitt Romney on Saturday called for the removal of the Confederate flag that flies outside the South Carolina state capitol in Columbia.

The flag is at the centre of a fierce political debate, in the aftermath of the shooting deaths of nine people at the historic Emanuel AME church in the city on Wednesday. The alleged gunman, 21-year-old Dylann Roof, who is white, was arraigned in court on Friday. All of those who died in the church were black.

At a Friday news conference Cornell William Brooks, the president of the National Association for the Advancement of Colored People, said: “The flag has to come down.

“This was not merely a mass shooting, not merely a matter of gun violence. This was a racial hate crime, and must be confronted as such … and that means, certainly symbolically, we cannot have the Confederate flag waving in the state capitol.”

On Saturday morning, using Twitter, Romney said: “Take down the #ConfederateFlag at the SC Capitol. To many, it is a symbol of racial hatred. Remove it now to honor #Charleston victims.”

In a previous comment on the shooting, issued on Twitter on Thursday, Romney said: “Heaven weeps again today, this time for God’s children killed in His Charleston house of prayer.”

Take down the #ConfederateFlag at the SC Capitol. To many, it is a symbol of racial hatred. Remove it now to honor #Charleston victims. — Mitt Romney (@MittRomney) June 20, 2015

The Confederate battle flag was moved to its position outside the state house, next to a monument to soldiers killed in the American civil war, in 2000. It previously flew from the roof.

One current Republican presidential candidate does not appear to agree with the former Massachusetts governor, who ran for the White House in 2008 and 2012, and President Barack Obama, who on Friday said the flag belonged in a museum.

At a vigil for the Charleston shooting victims on Friday, South Carolina US senator Lindsey Graham told the Guardian: “There are graveyards of Confederate soldiers all over the state – what do we do? How much of revisiting one’s past is it going to take before we can move forward? To the extent this debate helps us move forward, let’s have that debate.”

Graham and the other US senator from the state, Tim Scott, remained seated during standing ovations at the vigil, in response to calls from the podium for the flag to be removed.

Other 2016 contenders addressed the issue on Saturday. The former Hewlett Packard chief executive Carly Fiorina said the Confederate flag was a “symbol of racial hatred” but did not call for its removal. The only woman in the Republican race said her “personal opinion is not what’s relevant here”.

In a statement to the Associated Press, the Texas senator Ted Cruz said South Carolina did not need “people from outside of the state coming in and dictating” how it should resolve the issue.

Cruz also said he understood both sides of the debate – including those who saw the flag as a symbol of “racial oppression and a history of slavery” and “those who want to remember the sacrifices of their ancestors and the traditions of their states – not the racial oppression, but the historical traditions”.

A spokesman for Jeb Bush had no immediate comment. Bush ordered the Confederate flag removed from over the Florida statehouse in his first term as governor.

The Wisconsin governor, Scott Walker, and Ohio governor, John Kasich – neither confirmed as a candidate yet but both openly considering a run – ignored questions about the flag between Friday and Saturday. Spokesmen for most of the other Republican presidential contenders also either ignored such questions or formally declined to comment. They included the Louisiana governor, Bobby Jindal, former Arkansas governor Mike Huckabee, businessman Donald Trump and two serving US senators, Rand Paul of Kentucky and Marco Rubio of Florida.

A photograph posted to a website with a racist manifesto appears to show Dylann Roof, the suspect in the Charleston church massacre, posing with a Confederate flag. Photograph: Reuters

In 2007 Hillary Clinton, now the leading Democratic candidate for 2016, called for the flag’s removal, in part because she said the nation should unite under one banner while at war. Speaking in San Francisco on Saturday, she called for “commonsense” gun control legislation but did not address the flag issue.

Another GOP presidential contender, the former Texas governor Rick Perry, was criticised after he referred to the Charleston shooting on Friday as an “accident”.

“From the context of his comments, it’s clear Governor Perry meant ‘incident’,” a campaign spokesperson said.

On Saturday, at the Faith and Freedom Coalition Conference in Washington, Perry condemned the shooting but also repeated criticism of “the left” for what he said was its use of the Charleston shootings as a means to push for legislation on gun control.