CHICAGO — A top advisor to President Obama’s campaign lashed out at Mitt Romney on Sunday, arguing that the presumptive GOP nominee is misrepresenting a lawsuit Democrats filed in Ohio to equalize voting rights for all Ohioans.

The suit, which Romney has seized upon to argue that Obama is trying to undermine service members’ voting rights, calls for all Ohioans to be able to cast early votes up until the Monday before election day.

“What that lawsuit calls for is not to deprive the military of the right to vote in the final weekend of the campaign. Of course they should have that right. What that suit is about is whether the rest of Ohio should have the same right, and I think it’s shameful that Gov. Romney would hide behind our servicemen and women,” Obama campaign strategist David Axelrod said on “Fox News Sunday.”

Until 2011, all Ohioans could cast early ballots as late as the Monday before election day. Last year, the Legislature instituted a Friday cutoff for all voters except members of the military and their families.

In mid-July, the Obama campaign and state and national Democratic groups filed suit, arguing that a two-tier voting system was unconstitutional and calling for all voters to be allowed to cast ballots until the day before election day. The suit does not call for reducing early voting access for service members.

On Saturday, Romney accused Obama of trying to undermine service members’ voting rights, and he argued that Ohio was within its rights to give service members special privileges.

“President Obama’s lawsuit claiming it is unconstitutional for Ohio to allow servicemen and women extended early voting privileges during the state’s early voting period is an outrage,” Romney said in a statement Saturday. " …. If I’m entrusted to be the commander in chief, I’ll work to protect the voting rights of our military, not undermine them.”

The disagreement between the two camps hinges on the Constitution: Obama argues that all citizens must be afforded equal voting access, while Romney maintains that it is legal for active members of the military and their families to receive extra privileges.

“Making it easier for service men and women and their families to vote early is not only constitutional but commendable,” said Katie Biber, general counsel for the Romney campaign. “It is not a violation of the equal protection clause to give military voters special flexibility in early voting.”

A spokesman for the Obama campaign said Romney was trying to restrict access to the polls and was fabricating the notion that Democrats sought to restrict voting rights.

“The real story of what is happening in the Buckeye State is that Mitt Romney supports the Republican effort to stop people from voting by restricting their access to the polls,” Rob Diamond, the head of Obama’s veterans and military families coalition, said in a statement. “In 2008, more than 93,000 Ohioans utilized early voting in the three days before the election.”

The lawsuit and the reaction reflect the importance of Ohio and its 18 electoral votes in the upcoming election. It is a battleground state that voted for Obama in 2008 and that the Romney campaign is fiercely contesting. Early voters tend to be older citizens, women and the poor, of which the last two categories tend to favor Democrats.

seema.mehta@latimes.com