"Taking the next step toward a full NATO membership is of course important for Sweden and Finland. But it's also a very important step for NATO, because our countries will be security providers within NATO," Andersson told AFP in an interview.

Andersson rejected claims that she had conceded too much to Turkish President Recep Tayip Erdogan in order to convince him to drop his veto to Stockholm's membership.

"I think this is an agreement that I can stand fully behind," she said after lengthy talks in Madrid with Erdogan and her Swedish counterpart.

Andersson said she had been able to lay out to the Turkish leader changes in Sweden's terrorism legislation set to come into force next month.

"And of course, we will continue our fight against terrorism and as NATO members also do so with closer cooperation with Turkey," the Swedish premier said.

She insisted that Swedish authorities were working on extradition requests from Turkey in accordance with Swedish legislation and a European convention on extradition.

Andersson said she expected NATO leaders meeting Wednesday in Madrid to formally agree to invite Sweden and Finland to join the alliance without any surprises.

But she conceded that the process to become full members could take some time and throw up more hurdles.

"Thirty countries have to sign the accession of course and all 30 parliaments and you never know what's going to happen,"

"But I also know that the member states in NATO see the fact that Sweden and Finland both increase the security for NATO as a whole if we were to become members."