NATO chief Jens Stoltenberg, however, said he now expected Hungary's parliament to give a green light at the end of this month.
Sweden, along with Finland, applied to join the alliance in 2022 after Russia's invasion of Ukraine. But its membership has been held up by Turkey and Hungary, leaving the country in limbo and frustrating NATO allies, who see Sweden as a key player in ensuring security in the Baltic region.
Turkey's President Tayyip Erdogan signed Sweden's accession documents on Thursday, leaving Hungary as the last hold-out.
The Swedish and Hungarian prime ministers will meet next week at the European Council meeting in Brussels, but Kristersson said Sweden would not make any new promises on NATO.
"No demands that are related to NATO membership - that's not on the table," Kristersson told Sweden's TV4.
However, he said the two countries had much to discuss, including cooperation inside NATO, Hungary's upcoming EU presidency, support for Ukraine and how to get the widest synergies from their airforces sharing the same fighter jet programme - Sweden's JAS Gripen.
All of NATO's 31 members have to ratify an applicant country's accession before it can join the alliance and Orban has been angered by Swedish criticism of democratic developments under his government.
He has invited Kristersson to Budapest for negotiations over NATO, but he also repeated on Wednesday that his country supports Swedish membership.
Stoltenberg said he expected Hungary's parliament to ratify Sweden's accession when it reconvenes at the end of February.
"So we have to wait for that," Stoltenberg told reporters in Brussels on Friday.
"But I am absolutely confident and I count on Hungary that the ratification of Sweden will be ratified as soon as the parliament reconvenes at the end of February."
Kristersson said he did not know when Sweden would become NATO's 32nd member, but expected it to be "very soon".
(Reporting by Simon Johnson in Stockholm, Bart H. Meijer and Andrew Gray in Brussels; Editing by Ros Russell)
