David Cameron and the Danish prime minister, Helle Thorning-Schmidt, have brushed off criticism of their decision to pose for a “selfie” photograph at a memorial service for Nelson Mandela alongside the US president, Barack Obama.

The British prime minister said he was being polite when Thorning-Schmidt, the daughter-in-law of the former Labour leader Neil Kinnock, asked him to take part in the picture.

He told parliament on Wednesday: “In my defence I’d say that Nelson Mandela played an extraordinary role in his life and in his death in bringing people together.”

The photo went viral on Tuesday, prompting accusations from some of poor taste. Many noted that Michelle Obama looked on stony-faced during the rainy event in Soweto.

Thorning-Schmidt described her impromptu snap as “not inappropriate”.Speaking to the Danish media she said: “There were plenty of pictures that day. We’ve taken very many pictures of Obama, and I just think that it was kind of funny. It shows perhaps that when we meet from state and government, we too are just people who have fun together.”

She added: “There was obviously a sombreness but basically it was a festive event, which also celebrated a man who had lived for 95 years and achieved so much in his life. It was a big stadium, it was going on. There was singing and dancing, so there was a positive mood. And then we took a fun selfie.”

After the picture made headlines around the world, Cameron was challenged over his behaviour by Martin Horwood, a Liberal Democrat MP.

“Has the prime minister had the opportunity to discuss international mobile phone usage with any other European heads of government over the last day or so?” Horwood asked during the weekly prime minister’s question time in the House of Commons.

MPs laughed as Cameron replied: “You could say, in a roundabout way. Perhaps, in my defence, you should always remember that the television cameras are always on.

“But in my defence I would say that Nelson Mandela played an extraordinary role in his life and in his death in bringing people together. So of course when a member of the Kinnock family asked me for a photograph, I thought it was only polite to say yes.”

Earlier, the prime minister’s official spokesman declined to say Cameron regretted the behaviour or to accept the world leaders had been “larking around at a funeral”.

The photographer who took the picture of the three leaders posing for the selfie, Roberto Schmidt of the news agency AFP, said he felt the trio were “simply acting like human beings”.

Writing on the AFP correspondent blog, Schmidt said: “I took these photos totally spontaneously, without thinking about what impact they might have.

“At the time, I thought the world leaders were simply acting like human beings, like me and you. I doubt anyone could have remained totally stony-faced for the duration of the ceremony, while tens of thousands of people were celebrating in the stadium.

“For me, the behaviour of these leaders in snapping a selfie seems perfectly natural.”

Schmidt said it was wrong to suggest that Michelle Obama had been “rather peeved” at the group shot. “Photos can lie. In reality, just a few seconds earlier the first lady was herself joking with those around her, Cameron and Schmidt included. Her stern look was captured by chance.”

Reaction on social media in Denmark has been split between those who felt the mobile selfie was a gaffe, and others who pointed out that this was not actually a funeral and that the atmosphere in the World Cup stadium was decidedly upbeat.

The selfie, meanwhile, was a rare moment of glamour for Denmark’s PM amid domestic chaos. Earlier this week the justice minister resigned for allegedly lying to parliament. On Wednesday Denmark’s foreign secretary Villy Søvndal quit because of poor health.