Hungarian lawmaker Zsolt Nemeth said there was no need to convene an extraordinary session of parliament sooner to approve the decision as Turkish approval would come later.
Hungary's nationalist Prime Minister Viktor Orban has delayed ratification but his foreign minister earlier this month said that Budapest would not delay the process if Turkey dropped its opposition, which it did on Monday.
"We will take up work in mid-September," Nemeth, the head of Hungarian parliament's Foreign Affairs Committee, told private broadcaster InfoRadio.
There is no need to move sooner as Turkish President Tayyip Erdogan will not forward the ratification of Sweden's NATO membership to the Turkish parliament until it reopens in the autumn, he said.
Sweden and Finland applied for NATO membership last year in response to Russia's invasion of Ukraine, abandoning policies of military non-alignment that had lasted through the decades of the Cold War.
Ankara held out on the ratification for months, accusing Sweden of doing too little against people Turkey sees as terrorists, mainly Kurdish members of the outlawed Kurdistan Workers Party (PKK).
Hungary's ratification process has been stranded in parliament since last July, with Orban airing concerns about the Nordic countries' NATO membership.
Hungarian lawmakers approved Finland's bid in late March.
(Reporting by Gergely Szakacs; Editing by Mark Heinrich and Conor Humphries)
