The incident, which saw 11 Secret Service and five military personnel pulled from their security duties in Colombia at the Summit of the Americas, overshadowed the talks attended by Obama and other regional leaders.
The US Secret Service, which has sent the men back to the United States, is investigating claims they brought prostitutes to their hotel rooms here late Wednesday and had a dispute over payment with one of the women.
"I expect the investigation to be thorough and rigorous," Obama said Sunday at a press conference with Colombian President Juan Manuel Santos at the end of the summit.
"If it turns out the allegations that have been made in the press are confirmed, then of course I'll be angry."
The military is conducting a separate probe and has confined the service members involved to their barracks.
None of the Secret Service personnel involved -- both agents and uniformed officers -- was assigned to Obama's personal security detail.
But Obama, who is facing a tough reelection battle in November, stressed that all members of his traveling party should be on their best conduct as they represent the United States.
"My attitude with respect to the Secret Service personnel is no different than I expect out of my delegation sitting here. We're representing the people of the United States," he said. "And that means that we conduct ourselves with the utmost dignity and probity.
"What's been reported doesn't match up with those standards," the president added.
While prostitution is legal in designated areas in Colombia, such behavior would violate the agency's rules of conduct, in part because it could expose the agents to blackmail, facilitate espionage and help an enemy get inside a security perimeter, US congressman Peter King told The New York Times.
And Representative Darrell Issa, chairman of the House Oversight Committee, warned that more agents could be involved in the scandal, and expressed concern the incident might not be a one-off for the agency.
"The question is, is the whole organisation in need of some soul-searching, some changes?" the California Republican asked on CBS television's "Face the Nation."
"Things like this don't happen once, if they didn't happen before."
The New York Times quotes a senior US government official as saying the incident involved not just rank-and-file agents but also two Secret Service supervisors.
"It's just extremely poor leadership by them," the official told The Times.
White House spokesman Jay Carney insisted, however, that Obama had full confidence in the Secret Service and that the incident had no impact on the president's security.
US Southern Command chief General Douglas Fraser said Saturday that he was disappointed by the entire incident, saying the behavior was not in keeping with the professional standards expected of members of the United States military.
The Secret Service, which employs some 3,200 agents and 1,300 uniformed police, has been in the spotlight for a few notable incidents since Obama took office three years ago.
The last major lapse for the agency was in 2009, when aspiring reality television stars Tareq and Michaele Salahi crashed Obama's first White House state dinner in honour of India.
In November, an agent was charged with second-degree murder after an incident in Hawaii ahead of an APEC summit, The Washington Post reported, while another was charged with drunk driving in August while helping to arrange security for an Obama bus trip in Iowa.