"It is the Afghan public that will suffer another broken promise ... if the future plans of each candidate is not made clear standing side-by-side his or her rival," Ghani said on his website this week.
The Karzai team claimed that his policies were not ready and that Tolo TV, the network on which the debate was due to air, was biased against him, the London-based Guardian newspaper reported.
Karzai's campaign also said the president did not want to take part because all the country's 41 presidential candidates were not invited.
Jahid Mohseni, the chief executive of Moby Group, which owns the Persian-language Tolo TV, said the station hoped to hold a series of three debates, and that Karzai was welcome to join the remaining two.
Mohseni said negotiations over Thursday's debate began more than three weeks ago.
"Afghanistan's obviously a new democracy and we've got a lot of limitations in terms of communication and road structure," he said.
"We saw a TV debate as useful because it crosses barriers in terms of literacy, and candidates can talk to voters in their own homes."
Haroun Mir, deputy director of the Afghan Centre for Research and Policy Studies, said Karzai "knows very well that if he takes part in this debate he will face criticism of the two other candidates".
"For the past five years, as leader of Afghanistan, he has not been successful. It will be very difficult for him to defend what he has accomplished in the past five years. That's why he is trying to avoid direct debate," Mir told Al Jazeera.
Ghani still planned to take part in the televised debates, Ajmal Habidy, his aide, said.
"If President Karzai is not participating in the debates, it shows his weakness," he said.
Though Karzai's popularity has slipped in recent years, no challenger is expected to be able to defeat him in the election unless they combine their campaigns and back a single candidate.