Kristersson told reporters it had become increasingly clear in recent weeks that Turkey was ready to ratify Finland's bid, but still had reservations about Sweden's, meaning it could ratify Finland's first.
"We have no confirmation that will be the case, but we think that the overall assessment after many conversations recently is that the likelihood of this has increased," Kristersson said at a press conference.
Both countries have said they hope to be members by the NATO summit in Vilnius in July.
Finland and Sweden dropped their decades-long policies of military non-alignment and applied to join the alliance last May in the wake of Moscow's invasion of Ukraine.
Turkey and Hungary are the only NATO members still to ratify their bids, which must be accepted by all 30 existing members of the military organisation.
The Nordic countries coordinated their applications and up until this point NATO members have ratified both bids together.
Ankara suspended negotiations with Sweden in outrage after protests in January that included a Koran burning outside Turkey's embassy in Stockholm, but the talks resumed in Brussels on March 9.
Turkey has opposed the bids, accusing Sweden in particular of providing a safe haven for what it considers "terrorists", especially members of the Kurdistan Workers' Party (PKK).
Among other things, pro-Kurdish demonstrations in Sweden, where PKK flags have been common, have been a thorn in Ankara's side.
"Turkey still doesn't think we are all the way there, and that was clearly laid out at the meeting," chief Swedish negotiator Oscar Stenstrom said at the same press conference, adding that Ankara had not expressed the same "displeasure" toward Finland.
Meanwhile, Budapest is expected to vote in favour of both countries joining the alliance "in the coming weeks", the deputy speaker of the Hungarian parliament Csaba Hende said last week.
Kristersson also said he was confident that Sweden would eventually become a member of NATO.
"This isn't about if Sweden becomes a NATO member, but exactly when Sweden becomes a NATO member," he said.
He also stressed that with the security guarantees extended to Sweden during its application process, the country was "safer now than before we applied," and this would also be the case if Finland joined before Sweden.
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