"To accede to that instruction... would be to abdicate my responsibility," he said in the affidavit
Zuma, who last week beat back an attempt within ruling ANC party to unseat him, has been under pressure since the probe uncovered possible criminal activity in his relationship with the Guptas, a wealthy business family.
The president, who came to power in 2009, has faced growing calls to resign over multiple graft scandals and the country's poor economic performance, with unemployment at a 13-year high.
The watchdog instructed Zuma to set up a judicial inquiry into the allegations that the Guptas had influence over ministerial appointments and lucrative government contracts.
"To accede to that instruction... would be to abdicate my responsibility," he said in the affidavit quoted in South African papers on Sunday.
"(I) cannot be instructed by anyone as to when I should appoint a commission of inquiry."
The affidavit was lodged in Gauteng High Court on Friday.
"We look forward to opposing this application," the main opposition Democratic Alliance party said. "This is a desperate move by Jacob Zuma."
The ANC is due to elect a new leader at the end of next year, ahead of the 2019 general election when Zuma, 74, must stand down after serving two terms.