Former presidents George Bush Sr and Bill Clinton have joined forces to open a new centre in Arizona committed to encouraging civility in US politics, in the wake of the shooting of a Congresswoman Gabrielle Giffords.

The two are to serve as honorary chairmen of the centre, the National Institute for Civil Discourse, whose board will also include other prominent US political figures from both the Democratic and Republican parties.

Although there is no evidence that the the man suspected of the shooting, Jared Lee Loughner, was motivated by politics, the attack on the congresswoman opened a nationwide debate about whether politics in the US has become too polarised. There was special concern about the use of violent imagery and language that might encourage extremists.

Rightwing commentators at the time hit back, arguing that liberals were using the shooting, even though it was apparently not political, to smear conservatives.

The sheriff investigating the shooting complained at the time that political discourse in the country had become too extreme and there was an echo in this on Monday from the two former presidents.

Bush, in a statement at the opening of the new centre, said: "Our country needs a setting for political debate that is both frank and civil." Clinton said the new institute "can elevate the tone of dialogue in our country".

Among those who will serve on the board of the new centre will be the former supreme court justice Sandra Day O'Connor, the former Democratic Senate majority leader Tom Daschle, former secretary of state Madeleine Albright, former chief of staff to Ronald Reagan, Kenneth Duberstein, and Fox News anchor Greta Van Susteren.

About $1m (£616,000) has been raised for the centre, which will be funded by private donations.

Meredith Hay, provost of the University of Arizona, said that although the Tucson shootings were not linked to public discourse, they "created a space for us to think about civil discourse".

She told the Washington Post: "If anyone should lead this conversation, it should be the University of Arizona. We've lived through this terrible event and grown stronger through it. We have extraordinary scholars in the area of public discourse and public policy who can reach out nationally and create an exciting conversation."

One of the most prominent conservative talkshow hosts, Glenn Beck, has seen ratings plummet. It could be part of a backlash against his brand of conservatism in the wake of the Tucson shooting or his outspoken support for the outgoing Egyptian president Hosni Mubarak, though the downward trend began last year.

Sarah Palin also faced a backlash after the shooting over a list of Democratic targets, each marked with crosshairs, including Giffords, on her website. Two weeks after the shooting a poll showed 56% of respondents did not like her.