The morning meeting will focus on how the states and Washington can work together to spur economic growth, according to the White House.
The growing turmoil between Republican and Democratic governors over ballooning public employee pension benefits is not an agenda item, the White House said.
But Maryland Gov. Martin O'Malley's office said the friction won't be ignored.
O'Malley, who heads the Democratic Governors Association, will be recommending on Friday that Democratic governors increase their visibility on budget-balancing measures.
"We all have tough choices to make and we have made those choices in Maryland without attacking public employees ... though not necessarily to the benefit of public employees all the time," said O'Malley spokesman Shaun Adamec.
The Republican governors, who have attracted national attention over the past two weeks for their determined stance to cut public employee pensions, will be coming to Washington on Saturday for the annual National Governors Association conference.
The Republican Governors Association is pushing its support for scaling back public employee benefits. The group on Wednesday rolled out a Web site, called "Stand with Scott," to support Wisconsin Gov. Scott Walker's measures to rein in union power.
Texas Gov. Rick Perry, chairman of the GOP governors group, said Walker "is in the middle of what will be a defining moment for our country and the conservative movement." Nearly 52,000 people had "liked" the site on Facebook by Thursday evening.
Georgetown politics professor Stephen Wayne said he isn't expecting a showdown between opposing governor caucuses.
"The Republican governors obviously have a lot in common and the Democratic governors probably feel that the cuts can be Draconian, but in the end, they all have budget problems," he said.
Obama and O'Malley have recently been discussing ways to inject Democratic governors' budget solutions into the national dialogue, according to Adamec.
North Carolina Gov. Bev Perdue, Delaware Gov. Jack Markell and Massachusetts Gov. Deval Patrick are also among those attending Friday's meeting with the president.
The annual governors conference will feature a Sunday work session on pension obligations, led by municipal bond analyst Thomas G. Doe, founder and chief executive officer of Municipal Market Advisors. Doe said he will be urging governors to immediately address pension deficits or risk losing access to the municipal bond market.
"There is nothing that angers me more than people saying that the whole reason there is a pension problem is become of the subprime mess," Doe said. "It's important to remember that this all began in the 1960s when pensions became an exchange of union votes for a benefit. Over 50 years, that relationship has ended up in escalating into a very generous one."