Obama was to deliver remarks at campaign events in Delray Beach, Fla., and Dayton, Ohio. Vice President Joe Biden was to join him in Dayton.
Romney, the Republican presidential nominee, and running mate Paul Ryan were to speak at campaign events in Henderson, Nev., and Morrison, Colo.
Those states are considered swing states, or battleground states, where neither Obama nor Romney has overwhelming support.
The Monday night debate at Lynn University in Boca Raton, Fla., focused on foreign policy, but both candidates used their time to talk about domestic issues, including jobs, the economy and the budget. They also talked about the U.S. auto-industry bailout, school-class sizes and Romney's tax plan.
On foreign policy, Obama accused Romney of offering policies on the Middle East, Afghanistan, Iraq, Iran and elsewhere that were "all over the map."
"I know you haven't been in a position to actually execute foreign policy, but every time you've offered an opinion, you've been wrong," Obama said.
Romney countered that he didn't "see our influence growing around the world -- I see our influence receding, in part because of the failure of the president to deal with our economic challenges at home."
He congratulated Obama for the 2011 raid that killed al-Qaida terrorist leader Osama bin Laden, "But we can't kill our way out of this mess."
He said the Obama administration lacks "a comprehensive strategy" to diminish radicalism in the Middle East.
At one point, when Romney complained the U.S. Navy was "smaller now than any time since 1917," Obama said: "We also have fewer horses and bayonets, because the nature of our military's changed. We have these things called aircraft carriers, where planes land on them. We have these ships that go underwater -- nuclear submarines.
"And so the question is not a game of Battleship, where we're counting slips," Obama said.
He criticized Romney for once saying Russia was the biggest geopolitical foe facing the United States.
"The 1980s are now calling to ask for their foreign policy back because, you know, the Cold War's been over for 20 years," Obama said.