It is the latest in a series of challenges to Prime Minister Haider al-Abadi's reform efforts, which have run into problems due to the endemic nature of corruption in Iraq and the fact that officials are limiting their own privileges by implementing some changes.
The vice presidential positions, which came with large salaries and security details but few responsibilities, were most recently held by Nujaifi, a former parliament speaker, and ex-premiers Nuri al-Maliki and Iyad Allawi.
Nujaifi is seeking "to repeal the cabinet decision to cancel the position of vice president of the republic, and reverse (parliament's) decision to approve it," the Higher Judicial Council said in a statement.
The Supreme Court adjourned the case until November 24, the statement said.
Also Read
Nujaifi had earlier issued a statement saying he welcomed Abadi's reform efforts.
His case may be helped by the fact that the constitution mandates the existence of at least one vice president to fill in for the president if he is absent or his post becomes vacant.
In response to popular protests and calls from top Shiite cleric Grand Ayatollah Ali al-Sistani, Abadi announced reforms including scrapping the deputy premier and vice president posts, streamlining the cabinet, cutting salaries for officials and slashing their huge number of guards.
Parliament approved the measures along with its own series of proposed changes, but it has since pushed back against Abadi, complaining that its legislative power must not be usurped during the reform process.
Both Nujaifi's court case and the parliamentary complaint came after popular pressure for change decreased, with weekly protests that once drew thousands now dramatically smaller, if they take place at all.