"I take issue with President Obama's recent tour of apology," Romney said. "It's not because America hasn't made mistakes - we have - but because America's mistakes are overwhelmed by what America has meant to the hopes and aspirations of people throughout the world."
Obama has expressed regret while traveling abroad for America's leadership failures and other past conduct.
"This is the time for strength and confidence, not for apologizing to America's critics," Romney said.
Striking a hard line against Obama while speaking to the conservative Heritage Foundation, Romney said Britain's Guardian newspaper wrote that Obama has been more critical of his own country while on foreign soil than any other president in American history.
"The president also claimed on Arabic TV that America has dictated to other nations," Romney said. "No, America has sacrificed to free nations from dictators."
The speech was seen as a bid to enhance his foreign policy credentials among conservative Republicans. Romney has also been campaigning recently on behalf of Republican candidates in states such as Virginia and New Jersey.
Romney took aim at the Obama administration's push for new social spending, saying it could hurt defense programs and endanger America's national security.
"Backing away from missile defense and depleting the defense budget to fund new social programs, particularly in the face of global turmoil, would put America and Americans at risk," he said.
Romney branded Obama's proposal to cut missile defense programs a "grave miscalculation" in light of North Korea's provocations, Iran's near-nuclear status and Pakistan's instability.
Romney said Obama plans to shrink the defense budget every year over the next decade, from 3.8 percent of the economy down to 3 percent. He said the country should be spending more than 4 percent of the economy on defense.
"Arrogant, delusional tyrants can't be stopped by earnest words and furrowed brows," he said. "Action, strong bold action coming from a position of strength and determination, is the only effective deterrent."
Romney also urged Congress to fully fund and deploy a multilayered missile defense shield that he said was vital for the nation's security.
"I know the liberals have opposed missile defense ever since Ronald Reagan came up with it," he said. "But this is too big an issue for ideology or politics to prevail over national security."
Romney said liberals have long complained about too much defense spending.