Fedorov's surprise dismissal this month had sparked rare wartime protests prompting President Volodymyr Zelenskiy to replace his unpopular top general with a respected younger commander.
Zelenskiy said on Thursday he had offered Fedorov several other roles, including vice prime minister for defence innovation, but has not indicated he would reappoint him to the defence ministry.
Fedorov's refusal piles pressure on Zelenskiy, whom protesters gave a deadline of Friday to return the 35-year-old credited with cleaning up the defence ministry to his post.
Thousands of demonstrators have rallied in Kyiv and other cities over the past week to express anger over what they said was Zelenskiy's lack of communication over his decision making.
In a statement to reporters, Fedorov said only the positions of president, military chief and defence minister could "actually shape the course of the war".
"No other role carries the actual authority to combat procurement corruption, complete the army's transformation, plan and execute asymmetric operations against the enemy," he said.
Discussions between Zelenskiy and Fedorov were still ongoing, according to a source familiar with the matter.
"I think they will talk more," the source said.
Protest organiser Dmytro Koziatynskyi, a military veteran, said on Thursday that Fedorov had "done the right thing" by digging in.
"We must definitely push this appointment through," he wrote on X.
"There must be reforms in the MoD!"
The protests come at a precarious moment for Ukraine, which has been fighting for the upper hand against Russia since its full-scale invasion in 2022 but still faces unrelenting assaults on the battlefield and devastating air attacks on its cities.
Analysts say new top general Mykhailo Drapatyi, appointed on Tuesday, must manage a sprawling front and a manpower shortage while also building relations between army command and the defence ministry.
with AP
