Ulf Kristersson will receive the gift, his press secretary Hanna Strömberg tells Expressen.
"But it will come to Sweden in an orderly manner," she writes in a text message to the newspaper.
"It will not be taken to Sweden until all permits and papers are in order," she adds.
For now, it is being kept at the Swedish embassy in Ankara. There is no picture of the weapon, she says.
According to British Prime Minister Keir Starmer, the gift also included a box of ammunition. However, he says he cannot take the gift home due to the UK's strict gun laws.
