The cartoons have provoked a storm of protest in many Muslim countries, and have led to a boycott of many Danish products.
During a radio election debate with Moderate Party leader Fredrik Reinfeldt, Persson criticised Fogh Rasmussen for being too defensive in his reaction to the storm in the Muslim world.
He was asked what he would have done if a Swedish newspaper had published similar pictures.
“I would have called in the ambassadors from these countries, and explained the situation in Sweden,” he replied.
“I would have explained what freedom of the press is about, what democracy and the formation of public opinion mean for us and make it very clear that this has nothing to do with ridiculing or scoffing at another religion.”
While newspapers in a number of European countries have published the controversial cartoons, Swedish editors are taking a cautious line.
“We have not seen any reason to publish the pictures,” said Mats-Eric Nilsson, managing editor of Stockholm daily Svenska Dagbladet.
“We have taken into account the readers’ interest in seeing the pictures that are being discussed, and weighed that against the insult felt by many Muslims.”
But, he added, “we believe in wide-ranging freedom of expression. Those who want to publish them must be allowed to. It is unacceptable to use violence to try and limit that right.”
The editor of Dagens Nyheter, another Stockholm daily, said he saw “no particular reason” to buy the full rights to the material. But, Jan Wifstrand added, the paper had used its right to quote from other publications and shown some examples in order that readers could understand what all the fuss was about.
In the south of the country, near to the heart of the controversy in Copenhagen, Malmö-based Sydsvenska Dagbladet’s editor Peter Melin said he had not published the pictures. “I saw their publication as a provocation, and I still do,” he said.
Tabloid Expressen has published facsimiles of the pictures together with an opinion piece, which editor Otto Sjöberg justified as necessary “so that readers can understand what it’s about.”
Public service broadcaster SVT broadcast shots of the cartoons in a news report on the issue on Wednesday evening.
“We have not had any negative reactions,” Cilla Benkö, editor of news programme Aktuellt, told Svenska Dagbladet.