In a statement to the media on Saturday evening, Kurz said that he wanted to avoid months of chaos and stagnation, reports Xinhua news agency.
"My country is more important to me than my person," he said.
Kurz said that he would return to Parliament as the chairman of his conservative party and "use the opportunity to refute the allegations," which he claimed were "false".
Regarding appointing Schallenberg as his successor, Kurz said that the Foreign Minister had the diplomatic skills necessary to rebuild trust between the parties.
Kurz has been facing increasing calls for him to step down, including from his own government allies, as the 35-year-old Chancellor and nine others have been under investigation over claims that government money was used in a corrupt deal to ensure positive media coverage.
The opposition has called on Kurz to step down and has planned to take a no-confidence vote against him in Parliament on Tuesday.
Kurz is the youngest head of government in the world, and being first elected to the position at the age of 31 in January 2020, the youngest Chancellor in Austrian history.