Speaking on the sidelines of the G7 summit in Japan, Mr Obama said Mr Trump had shown a cavalier and ignorant attitude towards world affairs.
Mr Obama said foreign leaders were surprised by his nomination.
There has so far been no response from the billionaire businessman.
Donald Trump's controversial foreign policy pronouncements
- China is "raping" the US with its trade policy (May 2016)
- Relations with Russia and China will be improved "from a position of strength" (April 2016)
- China's membership of the World Trade Organisation has been a "total disaster" for the US, as has Nafta, a free trade agreement with Canada and Mexico (April 2016)
- Iran "cannot be allowed" to get a nuclear weapon (April 2016)
- America's allies are not paying their fair share of defence costs, especially Nato and Asian countries benefitting from US military support (April 2016)
- South Korea and Japan might need to develop their own nuclear arsenals (April 2016)
- Americans have "no choice" but to deploy 20,000-30,000 troops to Syria and Iraq to fight the Islamic State group (IS) (March 2016)
- The US should consider pulling out troops from Japan and South Korea if they did not pay the US more (March 2016)The president also downplayed Democratic party concerns about the long-running primary fight between Hillary Clinton and Bernie Sanders.He pointed out that occasionally in a primary "people get grumpy".But he insisted that one of the main differences between Democrats and Republicans this year was the fact that Democratic candidates were not so far apart ideologically.With Mr Trump's opponents for the Republican nomination dropping out of the race, he is now just a few votes short of securing the 1,237 delegates needed to officially become the Republican candidate for November's presidential election.
