After winning the backing of key powers, Rutte is the clear frontrunner to take over as head of the alliance when current leader Jens Stoltenberg's term ends this year.

But he has struggled to win over Orban and still faces competition from the only other candidate, Romanian President Klaus Iohannis.

"I'm cautiously optimistic about Hungary," Rutte told journalists after meeting Orban on the sidelines of an EU summit in Brussels.

Orban said this month he could drop his objections if Rutte apologises for previous comments slamming the right-wing government in Budapest, and allows Hungary to stay out of NATO's plans to boost aid for Ukraine.

Rutte said Orban "didn't ask for an apology, and I said that obviously I took note of what happened in Hungary in terms of societal reactions to what I said a couple of years ago".

"We left it at that, taking note of, and very much looking at the future and he didn't ask for any apology," Rutte said, adding that he would now write a letter to Orban summing up their talks.

For his part, Orban said Rutte could get his backing if he agrees to stick by a deal Stoltenberg struck in Budapest last week to grant Hungary an opt-out on NATO plans to aid Ukraine.

"If he's ready to support, we can go for it," Orban said.

"It's about the future, not about the past."

Leading NATO powers spearheaded by the United States are pressing to get an agreement on a new head of the alliance by a summit in Washington next month.

Rutte -- currently serving in a caretaker capacity as prime minister -- is set to leave his position in the coming weeks once a new Dutch government is installed.