Chief executive Dave MacKinnon and sacked manager Alex Rae
Alex Rae was sacked as Dundee manager because poor results were putting promotion at risk, the club has said.
Dundee chief executive Dave MacKinnon told BBC Sport that the four-man board decided to act following a run of nine games without a win.
"We felt there were signs against Ross County on Saturday that something had to be changed," he said.
MacKinnon said prospective candidates would have until Friday to register their interest in the vacant post.
Rae, 39, was dismissed on Monday, following the club's poor start to the season, which has seen them slip to third bottom of Division One.
Interview: Dundee chief executive Dave McKinnon
The Dens Park outfit remain just six points off the top, but McKinnon told BBC Sport it was time for a fresh approach as "the spark" was missing from the squad.
"It's never an easy time when a manager leaves. The board of directors met yesterday and we've had a string of nine games without a win," the chief executive said.
"We've dropped to eighth in the table and we've got aspirations to get back into the SPL. It's never easy and it's a very difficult time.
"But once you make the decision you have to be positive, move on and get back to where you want to get to."
We've got half a team out, but we still believe we have the players on the existing staff to gain promotion
Dundee chief executive Dave MacKinnon
Despite their indifferent form, MacKinnon conceded that injuries had played part in their current plight.
"We have been hampered by injuries. We've got half a team out, but we still believe we have the players on the existing staff to gain promotion."
MacKinnon said the club was now turning its attention to finding Rae's successor and would advertise the post on Wednesday, with the closing date for applications two days later.
"What we won't do is install someone just for the sake of having someone in place. Assistant manager Davie Farrell, who has done a really good job here, will take charge on Saturday.
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