Dodd became the first former Democratic presidential candidate to endorse Obama, just hours before Obama and Clinton were set to engage in the final televised debate before polls in Ohio and Texas.
Campaigning in the state of Ohio on Tuesday, Obama said: "I've told my staff and I'm sure Senator Clinton has told her staff, 'let's play to win, but let's make sure that we are maintaining the kind of campaign that, win or lose, it will be a campaign we are proud of'."
Obama, whose father came from Kenya, donned the clothes after being presented with them by tribal elders in a 2006 visit to the African state.
The Illinois senator said he expected there to be disagreements between the campaigns but that the photo was not indicative of Clinton's tactics.
"Certainly, I don't think that photo was circulated to enhance my candidacy, I think that's fair to say. Do I think that it is reflective of Senator Clinton's approach to the campaign?"
The row comes ahead of a crucial debate between the two on Tuesday in the key battleground state of Ohio.
Obama's aides had accused the Clinton camp of "shameful, offensive fear-mongering", saying the photo is a smear attempt as it plays on some US voters' belief that he is a Muslim, when in fact he is a practicing Christian.
Professor Abdallah Schleifer, a foreign policy specialist at the American University in Cairo, told Al Jazeera the photograph seemed to be a "desperate" attempt to tarnish Obama's image in the US.
"It's not simply a matter that it's a picture of Obama, dressed as - quote - a 'Somali elder' ... it includes a turban - he's wearing a turban," said Schleifer.
"Why is that a smear? Well ... You have to understand that in America there is a section of society for which terrorism and Muslims are associated together."
A Clinton campaign volunteer was sacked last year after circulating an email that falsely suggested Obama was a Muslim.
John McCain, the Republican frontrunner, also got involved in the controversy on Tuesday.
Bill Cunningham, a conservative radio talk show host who "warmed up" a crowd before McCain was to speak, used Obama's middle name, Hussein, three times as he addressed the audience.
Rumours about Obama having Islamic ties are circulating on the internet and some opponents have used his middle name to try to link him with former Iraqi leader Saddam Hussein.
Cunningham also suggested Obama was involved in shady deals.
The time will come, he said, when the media will "peel the bark off Barack Hussein Obama" and tell the truth about his relationship with indicted fundraiser Antoin "Tony" Rezko, who donated thousands of dollars to Obama's campaign that the candidate has since returned.
McCain quickly distanced himself from Cunningham and his remarks in Cincinnati.
"I apologise for it. I did not know about these remarks but I take responsibility for them. I repudiate them," he said.
Asked whether the use of Obama's middle name was proper, he said: "No, it is not. Any comment that is disparaging of either Senator Clinton or Senator Obama is totally inappropriate."
Obama's foreign policy adviser, Susan Rice, said the circulation of the photograph was divisive and suggests "that the customs and cultures of other parts of the world are worthy of ridicule or condemnation".
Howard Wolfson, a Clinton spokesman, said: "I just want to make it very clear that we were not aware of it, the campaign didn't sanction it and don't know anything about it."
Rivalry between Obama and Clinton in the race for the Democratic presidential nomination has become increasingly bitter in recent days and foreign policy has become a focal point.
In a speech in Washington DC on Monday, the former first lady criticised the Illinois senator's foreign policy experience, saying he had veered between pledging to meet leaders of nations such as Iran and Cuba as president to warning of US strikes on al-Qaeda targets in Pakistan.
Clinton has lost the last 11 Democratic presidential nominating contests to Obama and many analysts have said that she needs to win the forthcoming Ohio and Texas polls on March 4 to retain a chance of winning the nomination.
After a debate with Obama last Thursday in Texas in which she said she was honoured to share the stage with him, Clinton has toughened her message in the past few days.
A Quinnipiac University poll published on Monday showed Clinton leading Obama in Ohio by 51 per cent to 40 per cent among probable Democratic voters.
Two weeks ago, Clinton led by 55 per cent to 34 per cent, a sign that the momentum Obama has gained from 11 straight victories was paying dividends in the state.