Kurz, who has asked Austria's president to remove Interior Minister Herbert Kickl in the wake of a corruption scandal, told reporters in Vienna that vacant positions in government would be filled with civil servants and technocrats until the next elections, which are expected in a few months.
Austrian news agency APA reported that the FPO's ministers quit in unison on Monday.
Mr Kurz had responded to the scandal on Sunday by calling early elections.
New FPO leader Norbert Hofer, however, has said he will await ongoing talks involving all parliamentary parties and Van der Bellen, whom Kurz was due to meet at 12:30 p.m. (1030 GMT).
The FPO retaliated by withdrawing the rest of its ministers from the government, leaving Kurz without ministers for foreign affairs, defense, labor, and infrastructure.
FPO's Heinz-Christian Strache stepped down as vice-chancellor and party leader on Saturday after video published by German media appeared to show him offering government contracts in return for campaign help to a fake Russian backer in a villa on the Spanish resort island of Ibiza.
Chancellor Kurz (VPO) said he was "shocked" by Strache's behaviour, describing it as "a wrong approach to politics" - a masterly understatement - which had damaged Austria's worldwide reputation.More news: Family of murdered pregnant teen demands answers from hospital
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Bluemel cited a need to get the bottom of the scandal triggered by a video, leaked to two German publications, in which Strache and party colleague Johann Gudenus are heard telling a purported Russian investor that she can expect lucrative construction contracts if she buys an Austrian newspaper and supports the Freedom Party.
"It would be nearly naive for Kurz to assume that we, the FPO, have no distrust of him following his distrust in us", Oesterreich quoted Kickl as saying.
Kickl was FPO's secretary-general at the time when any political donations would have been made.
Meanwhile, in the UK, Brexit Party leader Nigel Farage is facing fresh scrutiny over his finances.
Kurz has pledged a full investigation into any crimes or wrongdoing arising from the footage, which was filmed in 2017.
Kurz has said the recordings were the final straw in a string of FPOe-related scandals, which have dogged the coalition since its formation in late 2017.
In 2016, the FPO signed a cooperation agreement with Putin's United Russia party.