Trump, the billionaire US real-estate mogul and reality TV star, has dominated headlines since launching his presidential campaign last year with a mix of incendiary comments and policy stances seen as insulting Mexicans, Muslims and women, among others.
He has proposed building a giant wall along the US border with Mexico to keep out illegal immigrants and vows that he will get the southern neighbour to pay for it.
"They are not sure how seriously to take some of his pronouncements," Obama told reporters on the sidelines of the Group of Seven summit, referring to global leaders.
"But they're rattled by them, and for good reason," he added.
"Because a lot of the proposals that he has made display either ignorance of world affairs or a cavalier attitude or an interest in getting tweets and headlines".
Trump has disdained the usual cautiousness of past candidates for the country's highest office - Republican or Democrat - who while appealing to their base constituencies have often tried to take positions closer to the centre that would appeal to broad cross sections of the electorate.
But recent opinion polls show Democrat Clinton and Trump in an increasingly tight race were they to meet, as expected, in November's election after winning formal nominations at their party conventions this summer.
Clinton is vying to become the first female president in US history and while she leads challenger Bernie Sanders, the Vermont Senator has remained competitive and drawn support from younger voters.
Obama tried to downplay the rivalry.
"What is really important to remember is that unlike what you have seen in the Republican primary, for the most part there is not that big a difference in terms of the issues.
"They are both good people, I know them both well," he said of Clinton and Sanders, both of whom he served with in the Senate.
He called it "important for us to try to end this in a way that leaves both sides feeling proud of what they have done".