In February, the United States, Britain, France and Germany backed Rutte to succeed Jens Stoltenberg as the head of NATO, putting him in a strong position to win the leadership of the transatlantic alliance.
On Tuesday, however, Iohannis said he will compete for the post, arguing Eastern European states need better representation in Euro Atlantic leadership roles.
"The time has come ... for our country to take on greater responsibility within euroatlantic leadership structures," Iohannis told reporters.
"I think NATO needs to renew its outlook on its mission. Eastern Europe has a valuable contribution in NATO talks and decisions. With a balanced, strong and influential representation from this region, the Alliance will be able to make the best decisions to answer all member states' needs and concerns."
NATO leaders are appointed by consensus, meaning all members must consent to a final decision. The alliance has 32 members following Sweden's recent accession.
Diplomats have said Rutte was the only official candidate for the post in the behind-the-scenes contest, although some said Iohannis' name had also been floated in informal discussions.
European Union and NATO state Romania has raised defence spending to 2.5% of gross domestic product in response to Russia's invasion of Ukraine.
The country, which shares a 650km (400 mile) border with Ukraine, is host to a U.S. ballistic missile defence system and a permanent NATO battle group.
(Reporting by Luiza Ilie, editing by Ed Osmond)
