Romney called the report "devastating" and said the figures provide more evidence that Obama's economic policies are failing.
"We should be well into a very robust recovery by now," Romney said on CNBC.
The presumptive Republican nominee said Obama has spent too much time focused on initiatives like health care reform, which he said have suppressed hiring.
Obama, meanwhile, said during an event in Minnesota Friday that the economy is creating jobs, "we're just not creating them as fast as we want."
"From the moment we first took action to prevent another depression, we knew the road to recovery would not be easy, we knew it would take time, we knew there would be some bumps along the way," he said, adding that he believed "if we were willing to roll up our sleeves and never quit, we just wouldn't come back, we'd come back stronger than ever."
"That continues to be my belief," Obama said. "We will come back stronger, we do have better days ahead."
The Labor Department reported Friday morning US nonfarm payrolls rose by a scant 69,000 in May, the smallest gain in a year, and the unemployment rate unexpectedly ticked higher to 8.2 percent from 8.1 percent.
House Majority Leader Eric Cantor (R-Va.) described the jobs report as "pathetic."
US stocks were down sharply on the news, with the Dow Jones Industrial Average turning negative for the year after plunging more than 200 points.
The White House fought back against the criticism, arguing that the economic crisis predates Obama's election.
"Problems in the job market were long in the making and will not be solved overnight," wrote Alan Krueger, chairman of the Council of Economic Advisers, in a statement posted by the White House. "The economy lost jobs for 25 straight months beginning in February 2008, and over 8 million jobs were lost as a result of the Great Recession."
Republican leaders, however, dismissed the White House's defense.
"It is clear that the policies we've seen are not working," said House Speaker John Boehner (R-Ohio), according to The Wall Street Journal. "The American people are in a desperate situation. It's time for us to change course."
Boehner also criticized Obama for spending time on the campaign trail as the economy is floundering.
"Maybe the president ought to get out of the badminton game and get into the rugby match that is right in front of him," he said.
Obama's Friday schedule is bound to fuel that criticism, with the president set to attend a series of big-ticket fundraising events in Minneapolis and Chicago, FOX News Channel reported.