Defence Minister Karin Enstrom declared Sweden's interest in a letter to the Nato chief of staff, stating that the purpose is to deepen cooperation with Nato and especially to participate in advanced training.
"Nato has said it will happen in the context of the NRF," says Enstrom.
The government has wanted Swedish troops to join the Response Force since 2008 but it has hitherto been impossible as there was insufficient support in parliament, although Foreign Minister Carl Bildt has claimed that it was more a question of "technology over politics".
Neighbouring Finland has already joined the force.
The Social Democrats only last week shifted their position on the issue and underlined the importance of Swedish troops taking part in the Nato force.
"I think it's great that they've come to the right conclusion, even if it has taken time," Bildt said.
Alliance government coalition partners the Centre Party, previously doubtful of Swedish participation in the NRF, has also now backed the move, saying that Swedish soldiers need to train in complex situations.
"Finland is already involved and the defence forces need to sharpen their skills by participating in advanced exercises," said Centre Party defence spokesman Staffan Danielsson.
Danielsson expressed regret that while Sweden moves closer to Nato integration there is no impartial analysis of what a formal membership could mean.
"It is incomprehensible that the Social Democrats refuse to countenance this," he said.
The Nato Response Force was formed in 2006 and consists of 13,000 soldiers as well as aircraft and ships. Nato countries take turns to participate in the force, which can be deployed on short notice across the world.
Partner countries, such as Sweden, may also contribute. They retain the right to decide whether to participate in a mission, even after having registered units to the NRF in advance.
The Armed Forces will shortly submit proposals to the government on what Sweden would be able to contribute with from 2014 onwards. For 2014, discussions have concerned de-mining units and air surveillance and in the longer terms ships, helicopters and the Gripen fighter jets may take part.
According to discussions, Sweden will provide army units at the earliest in 2017.
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