A day after falsely suggesting there was an immigration-related security incident in Sweden, President Donald Trump said his comment was based on a television report he had seen.

Trump, who in his first weeks in office has tried to tighten US borders sharply for national security reasons, told a rally on Saturday that Sweden was having serious problems with immigrants.

"You look at what's happening last night in Sweden," Trump said. "Sweden. Who would believe this? Sweden. They took in large numbers. They're having problems like they never thought possible."

No incident occurred in Sweden and the country's baffled government asked the US State Department to explain.

"My statement as to what's happening in Sweden was in reference to a story that was broadcast on @FoxNews concerning immigrants & Sweden," Trump said in a tweet on Sunday.

Sweden's crime rate has fallen since 2005, official statistics show, even as it has taken in hundreds of thousands of immigrants from war-torn countries like Syria and Iraq

Fox News, a US channel that has been cited favourably by Trump, ran a report Friday about alleged migrant-related crime problems in the country.

A White House spokeswoman told reporters last night that Trump had been referring generally to rising crime, not a specific incident in the Scandinavian country.

Sweden's crime rate has fallen since 2005, official statistics show, even as it has taken in hundreds of thousands of immigrants from war-torn countries like Syria and Iraq.

Trump's comment confounded Stockholm. "We are trying to get clarity," Foreign Ministry spokeswoman Catarina Axelsson said.

Sweden's embassy in the United States repeated Trump's tweet about having seen the Fox report, and added, "We look forward to informing the U.S. administration about Swedish immigration and integration policies."

Trump has been widely criticized for making assertions with little or no supporting evidence.

He has said more than 3 million people voted fraudulently in the U.S. election, which officials say is false, and incorrectly stated that he won by the most decisive margin in decades.

Swedish Foreign Minister Margot Wallstrom appeared to respond to Trump on Saturday by posting on Twitter an excerpt of a speech in which she said democracy and diplomacy "require us to respect science, facts and the media."

Her predecessor was less circumspect.

"Sweden? Terror attack? What has he been smoking? Questions abound," former Foreign Minister Carl Bildt wrote on Twitter.

Other Swedes mocked Trump by posting pictures of reindeer, meatballs and people assembling IKEA furniture.

"#lastnightinsweden my son dropped his hotdog in the campfire. So sad!" Twitter user Adam Bergsveen wrote.

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