Dutch Prime Minister Mark Rutte will succeed Jens Stoltenberg as Nato chief, Dutch national broadcaster NOS reported on Tuesday.
Mr Stoltenberg neither confirmed nor denied the media report during a news conference alongside US Secretary of State Antony Blinken in Washington.
"With the announcement of [the support of Hungarian] Prime Minister [Viktor] Orban, I think it's obvious that we are very close to a conclusion to select the next secretary general, and I think that's good news," Mr Stoltenberg told reporters, while praising Mr Rutte.
"I think Mark is a very strong candidate. He has a lot of experience as prime minister.
"He's a close friend and colleague, and I therefore strongly believe that very soon, the alliance will have decided on my successor," he said.
"And that will be good for all of us, for Nato and also for me."
Hours earlier, Hungary and Slovakia had given their support to the candidacy of Mr Rutte, clearing a crucial hurdle on his way to Nato's top job.
Nato's next secretary general will face the challenge of sustaining allies' support for Ukraine's fight against Russia's invasion, while guarding against any escalation that could draw the military alliance directly into a war with Moscow.
Since Russia launched its full-scale invasion over two years ago, Rutte has been one of the driving forces behind Europe's military support to Ukraine, repeatedly stressing a need for a Russian battlefield defeat to secure peace in Europe.
Under his recent leadership, the Netherlands has ramped up defence spending, providing F-16 fighter jets, artillery, drones and ammunition to Kyiv as well as investing heavily in its own military.
Nato takes decisions by consensus, so any candidate needs the support of all 32 allies. Only Romania, whose President Klaus Iohannis is also vying for the job, is still officially opposed to Mr Rutte's candidacy.
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Hungary's backing followed a meeting between Mr Orban and Mr Stoltenberg last week, where the two sides agreed that Hungary would not block Nato decisions on providing support for Ukraine but agreed that it would not be involved.
"PM Mark Rutte confirmed that he fully supports this deal and will continue to do so, should he become the next secretary general of Nato," Mr Orban wrote on X.
"In light of his pledge, Hungary is ready to support PM Rutte’s bid for Nato secretary general."
Mr Orban had earlier opposed Mr Rutte's candidacy because he had expressed "problematic" opinions that included the idea that Hungary should leave the EU.
Hungary has been at odds with other Nato countries over Mr Orban's continued cultivation of close ties with Russia and refusal to send arms to Ukraine, with Budapest's foreign minister last month calling plans to help the war-torn nation a "crazy mission".
Turkey and Slovakia have also changed course on Mr Rutte's bid, with Turkey saying it would support him in late April and Slovakia announcing its support earlier on Tuesday.
Slovakia, which borders Ukraine, had stressed the need for the next Nato chief to help deal with the protection of Slovak airspace, its President Peter Pellegrini said, after the previous Slovak government donated an S-300 system to Ukraine, and allies pulled out Patriot batteries that had been temporarily placed there.
Mr Stoltenberg's term will end on October 1, 10 years after taking office in 2014, only a few months after Russia annexed Crimea.
During his tenure, Mr Stoltenberg oversaw Nato's shift from an alliance mainly engaged in crisis management missions in far-off places such as Afghanistan back to its roots of defence against Russia.
Four countries have joined Nato since Mr Stoltenberg took office - Montenegro, North Macedonia, Finland and Sweden.
