In a letter to Orban, Kristersson said he would also accept an invitation received earlier this week to meet in Budapest "at a time convenient for both of us".
"I agree with you that a more intensive dialogue between our countries would be beneficial," Kristersson said in the letter.
Sweden applied to join NATO in 2022 after Russia's invasion of Ukraine, but its application has been held up by Turkey and Hungary.
On Tuesday, Turkey's parliament gave the green light to Sweden's application and President Tayyip Erdogan is expected to add his signature in the coming days.
That will leave Hungary as the only NATO member not to have ratified Sweden's membership.
On Tuesday, Orban invited Kristersson to Budapest to negotiate his country joining the bloc. Hungary's parliament is in recess until around mid-February.
Hungary's parliamentary speaker said on Thursday there was no urgency in approving Sweden's NATO membership bid.
Turkey and Hungary maintain better relations with Russia than other members of the U.S.-led North Atlantic Treaty Organization.
(Reporting by Simon Johnson, editing by Terje Solsvik)
