Following Turkey's ratification last month, Hungary remains the last NATO member stopping Sweden from joining the alliance.
After Russia's invasion of Ukraine, Sweden applied to join NATO in May 2022, at the same time as Finland.
Although it says it supports Stockholm in principle, Budapest prolonged the process by asking Sweden to stop "vilifying" Orban's nationalist government.
Kristersson's talks with Orban in Budapest will include "defence and security policy cooperation between Hungary and Sweden," the Swedish government said in a statement.
Orban wrote on X, formerly Twitter, that it would be his "pleasure" to welcome Kristersson to Budapest.
Hungary's parliament will vote on Sweden's NATO bid on Monday.
Earlier, when announcing the vote, Mate Kocsis, leader of the ruling party Fidesz parliamentary group, said his group "intended to support" Sweden's membership.
- Rebuild trust -
Orban announced on Saturday that Hungary was "on course" to ratify Sweden's bid.
"The good news is that our current dispute with Sweden is moving towards a conclusion," he sad.
"Together with the Swedish PM, we have taken important steps in order to rebuild trust," he said, without giving details.
Asked about the remarks, Kristersson said Monday that he did not know what Orban had meant.
"I simply think there is a strong will to finalise this process of NATO accession," Kristersson said.
Swedish officials have insisted there would be no negotiations on ratification. Orban at first posted on X, the former Twitter, that he invited Kristersson to "negotiate".
In an invitation letter, he did not use the word "negotiate" but said he was inviting him to "exchange views on all issues of common interest".
Budapest has often denounced what it called Sweden's "openly hostile attitude", accusing Swedish representatives of being "repeatedly keen to bash Hungary" on rule-of-law issues.
Since Orban returned to power in 2010, the nationalist premier has cemented his power with critics accusing him of democratic backsliding.
Orban -- the sole EU leader to have maintained ties with the Kremlin after the invasion of Ukraine -- also frequently clashes with Brussels over rule-of-law, LGBTQ and asylum seeker rights and other issues.
Brussels has frozen billions of euros amid suspicions that European funds were being misused.
Polish Prime Minister Donald Tusk on Monday criticised Hungary's "unacceptable" delay in ratifying Sweden's NATO accession with the Russia-Ukraine war raging.
Over the weekend, a group of bipartisan US senators visited Hungary to press the country over Sweden's bid. The government refused to meet with them.
NATO membership applications require unanimous ratifications by all alliance members.
Finland became the 31st member of the military alliance in April.
bur-jza/tw
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