"As we look ahead to the challenges that we face as a nation and the leadership that's required, you don't just have my words, you have my deeds," Obama told the Veterans of Foreign Wars. He jabbed often at Romney without ever naming him.
With both men were going after the military vote, the Democratic president sought to make the most of his signature national security policies, chiefly ending the unpopular war in Iraq, winding down the war in Afghanistan and the killing of al-Qaida terrorist leader Osama bin Laden.
He mocked Romney's opposition to the 2014 timeline for ending the Afghan war, saying: "When you're commander in chief, you owe the troops a plan."
For at least one week, foreign policy moved near the front of the economy-oriented campaign, as presumptive Republican nominee Romney was heading to England, Israel and Poland to show some standing on the world stage. Obama's address to the veterans group was intended, in part, to undercut that trip before it began by raising doubts about Romney's readiness.
Romney was to address the VFW on Tuesday, before leaving the country.
The Republican, too, was back at the rhetorical attack.
While his campaign popped out press releases about "another dismal day in the Obama economy," Romney was telling donors in California that Obama is "out of ideas and out of excuses."
Still in the shadow of a rampage that united the nation in grief, both campaigns weighed how much and how fast to calibrate their tones. They seemed intent on returning to the business of defining their message and their opponents, albeit not quite yet with the vitriol of earlier weeks.
The race is tight, both nationally and in the select states expected to decide the outcome, polls show.
That leaves little time for either side to dial down.
Obama tried to put the squeeze on Romney, with the president's campaign aides demanding "substantive" expectations for Romney's upcoming trip abroad.
In a conference call with reporters, Obama campaign officials challenged Romney to offer specific policy ideas during the trip. Romney's travels are highly anticipated as a measure of how well he can stand up on the world stage. Obama took an even broader such trip as a candidate in 2008.
"If Romney wants to be president, if he is ready to be commander in chief, he needs to prove that he's willing to have open and honest discussions about his world views, about his beliefs, about his policies with some of our strongest allies," said Michele Flournoy, a campaign adviser and former top policy official at the Pentagon.
Four years ago, trying to burnish his own credentials against military hero Sen. John McCain, Obama traveled extensively to the Middle East and Europe, with stops in both war fronts of Afghanistan and Iraq. Obama adviser Robert Gibbs said the question for Romney is whether his trip "will be similar substantively" for voters.
In California, Romney was raising money in the wealthy and Republican heavy area of Orange County on Monday after holding three fundraisers in the San Francisco Bay area the previous night.
He was expected to raise $10 million during the swing.
Obama is on a previously scheduled three-day trip that includes campaign fundraisers Monday in California and Tuesday in Seattle. He was expected to raise more than $6 million on the West Coast.
Both campaigns were keeping their largely negative television advertisements off the air in Colorado, a key battleground state in the November election.
The Obama campaign on Monday released a new television advertisement casting the election as a choice between two contrasting economic visions. The ad had a softer tone than many of the campaign's previous spots.
"Sometimes politics can seem very small. But the choice you face, it couldn't be bigger," Obama said in the ad, which was to air in nine battleground states, including Colorado. The campaign said the ad would not start running there until Saturday in keeping with its decision to take down its advertising in the state this week in response to the shooting.
The presidential race resumed as the accused Colorado shooter appeared in court Monday for the first time.
Vice President Joe Biden, campaigning for his boss in Florida, jettisoned his typical speech to focus on the shooting victims and the stories of heroism from that night.
Beaumont reported from Irvine, Calif. AP writers Ben Feller and Mark S. Smith in Washington, Matt Sedensky in Manalapan, Fla., and Sandra Chereb in Reno, Nev. contributed to this report.