Swedes, and some Americans, have been wondering about representations of the Nordic nation in the US since Donald Trump invoked "what's happening last night in Sweden" while alluding to past terror attacks in Europe during a rally on February 18.

There had not been any major incident in Sweden the previous night.

Then, Fox News commentator Bill O'Reilly convened an on-air face-off on Thursday over Swedish immigration and crime between a Swedish newspaper reporter and a man identified on-screen and verbally as a "Swedish defence and national security adviser", Nils Bildt.

Mr Bildt linked immigration to social problems in Sweden, lamented what he described as Swedish liberal close-mindedness about the downsides of welcoming newcomers and said: "We are unable in Sweden to socially integrate these people", arguing that politicians lacked a systematic plan to do so.

But if viewers might have taken the "adviser" for a government insider, the Swedish Defence Ministry and Foreign Office told the Dagens Nyheter newspaper they knew nothing of him.

Mr Bildt is a founding member of a corporate geopolitical strategy and security consulting business with offices in Washington, Brussels and Tokyo, according its website.

His biography speaks of expertise on defence and national security issues, saying his experience includes serving as a naval officer, working for a Japanese official and writing books on issues ranging from investment and political climates to security issues in working in hostile environments.

But security experts in Sweden said he was not a familiar figure in their ranks.

"He is in not in any way a known quantity in Sweden and has never been part of the Swedish debate," Swedish Defence University leadership professor Robert Egnell said.

He and Mr Bildt - also known then as Nils Tolling - were in a master's degree programme in war studies at King's College London, in 2002-2003, and Mr Bildt moved to Japan soon after, he said.

The executive producer of The O'Reilly Factor said Mr Bildt was recommended by people the show's booker consulted while making numerous inquiries about potential guests.

"After pre-interviewing him and reviewing his bio, we agreed that he would make a good guest for the topic that evening," executive producer David Tabacoff said.

The network said Mr O'Reilly was expected to address the subject further on Monday's show.

Mr Bildt did not respond to email inquiries on Saturday but a person who answered the phone at his company agreed to relay one.

Mr Bildt told the Dagens Nyheter newspaper on Friday that he was a US-based independent analyst, and Fox News had chosen its description of him.

"Sorry for any confusion caused, but needless to say I think that is not really the issue," he said.

"The issue is Swedish refusal to discuss their social problems and issues," he added, in a statement to the news website Mediaite, explaining his profession as being an independent political adviser.

President Trump's initial remark about "last night in Sweden" sparked a burst of social media mockery, while Mr Trump explained on Twitter that he was referring to a Fox News piece on immigration and Sweden that he had seen the night before.

Mr Trump and his supporters, though, saw vindication when a riot broke out on Monday after police arrested a drug suspect in a predominantly immigrant suburb of Stockholm.

Cars were set on fire and shops looted, but no one was injured.

Mr Trump took to Twitter again on Monday to declare that large-scale immigration in Sweden was "NOT!" working out well, upsetting many Swedes.