NATO chief Jens Stoltenberg said Monday that Sweden's accession to the alliance shows Russian President Vladimir Putin "failed" in his Ukrainian war strategy of weakening it.

The Kremlin's invasion not only prompted formerly non-aligned nations Sweden and Finland to come under NATO's defence umbrella, but now "Ukraine is closer to NATO membership than ever before," Stoltenberg said.

His comments, made next to Swedish Prime Minister Ulf Kristersson, came just before Sweden's flag was to be run up a flagpole outside NATO's Brussels headquarters in a ceremony sealing Sweden becoming the alliance's 32nd member country.

"When President Putin launched his full-scale invasion two years ago, he wanted less NATO and more control over his neighbours. He wanted to destroy Ukraine as a sovereign state, but he failed," Stoltenberg said.

"NATO is bigger and stronger," he said.

Stoltenberg added that he "didn't expect" to see Finland and Sweden join during his time as the alliance's secretary general.

"Of course this changed totally with the full-scale invasion of Ukraine and since then things really moved very quickly."

Finland joined NATO last year, swiftly after applying.

Sweden's adhesion took longer as NATO members Turkey and Hungary held up the process. But Ankara in January and Budapest last week finally gave their formal assent.

Kristersson said Sweden now "will share burdens, responsibilities -- and risks -- with our allies".

"The security situation in our region has not been this serious since the Second World War, and Russia will stay a threat to Euro-Atlantic security for a foreseeable future," he said.

For Russians, Putin has framed his 2022 all-out invasion of Ukraine as a defensive "military operation" against an expanding NATO.

The members of the US-led alliance have lent their military and financial support to Kyiv in its fightback. But momentum is slowing as US political will fractures and Europe struggles to meet Ukraine's ammunition needs.

Stoltenberg said that a negotiated peace was possible for Ukraine -- but only if Putin pulls his forces back.

"President Putin started this war and he could end it today. But Ukraine does not have this option. Surrender is not peace," the NATO chief said.

"We must continue to strengthen Ukraine to show President Putin that he will not get what he wants on the battlefield, but must sit down and negotiate a solution."

On Ukraine or other countries wanting to join the alliance, Stoltenberg said that "NATO's door is open".

"It's not for Russia to decide which path different European countries wants to choose," he said.