All but two of NATO's 31 members -- Turkey and Sweden -- have signed off on Stockholm's push for membership.
"The Hungarian Government has repeatedly said that it will not be the last NATO ally to ratify Sweden's accession," Stoltenberg said at talks with Hungary's president in Brussels.
"Now I count on Hungary to fulfil that commitment. The Hungarian parliament should vote to ratify without further delay."
Turkish President Recep Tayyip Erdogan officially submitted Sweden's NATO membership application to parliament last month.
Hungarian President Katalin Novak, whose role is largely ceremonial, said she personally backed Sweden's bid, but it was up to Hungary's parliament to approve it.
"Some of the Hungarian parliamentarians argue that Sweden is or has been quite vocal in condemning the functioning of the Hungarian parliament," Novak, a close ally of Prime Minister Viktor Orban, said.
Sweden and its nordic neighbour Finland dropped their long-standing policies of non-alignment in the wake of Russia's invasion of Ukraine last year and asked to join NATO.
Finland became NATO's 31st member in April.
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