By convention, former presidents tend to leave the political fray and avoid commenting on their successors.
Speaking at a news conference at the Apec summit in Lima, Peru, Mr Obama said he intended to assist Mr Trump and give him time to outline his vision.
But he said that, as a private citizen, he might speak out on certain issues.
“I want to be respectful of the office and give the president-elect an opportunity to put forward his platform and his arguments without somebody popping off,” Mr Obama said.
But, he added, if an issue “goes to core questions about our values and our ideals, and if I think that it’s necessary or helpful for me to defend those ideals, then I’ll examine it when it comes”.
The president described himself as an “American citizen who cares deeply about our country”.
Speaking at a news conference to mark the end of the Asia-Pacific Economic Cooperation (Apec) summit, Mr Obama reiterated that he would extend to Mr Trump’s incoming administration the same professional courtesy shown to his team by his predecessor George W Bush.
Mr Bush has refrained since leaving office from commenting on Mr Obama’s presidency. “I don’t think it does any good,” he told CNN in 2013, after Mr Obama was elected for a second time.
“It’s a hard job. He’s got plenty on his agenda. It’s difficult. A former president doesn’t need to make it any harder. Other presidents have taken different decisions; that’s mine.”
Mr Bush’s stance falls in line with tradition. US presidents tend to avoid criticising predecessors or successors. Mr Obama was clear that he would not weigh in on Mr Trump’s decisions while he is still in office.
But his suggestion that, as a private citizen, he would seek to defend “core values” comes amid mounting concern among civil rights groups and others about Mr Trump’s political appointments.
The president-elect’s chief strategist, Steve Bannon, was previously the head of Breitbart, a website which has been accused of promoting racism and anti-Semitism. And Mr Trump’s national security adviser, General Michael Flynn, has previously likened Islam to a “cancer” spreading through the US.
Mr Trump’s nominee for attorney general, Jeff Sessions, was rejected from becoming a federal judge in 1986 because of alleged racist remarks.
Mr Obama said he believed that the intense responsibility of the presidency would force Mr Trump to moderate some of the more extreme policy positions he advocated during his campaign. ‘Smarter message’
Asked about the failure of the Democratic party’s campaign under Hillary Clinton, Mr Obama was critical of what he described as the “micro-targeting” of “particular, discreet groups”, rather than reaching out to the entire country.
Mrs Clinton has been criticised for focusing her energy on certain demographics, including Latinos and women, who were believed to support her, at the expense of a broader campaign.
That approach “is not going to win you the broad mandate that you need”, Mr Obama said, adding that the party needed a “smarter message”.–BBC
