"It was ambitious for the legislature to think 21 days would be enough," Chiwesh told the state run Sunday Mail newspaper.
He also said there are legal provisions to extend the period before the election is held.
"We want to make it clear we intend to hold the run-off at the earliest date because the period set by the legislature shows that it should be held as soon as possible."
The electoral body is waiting for the government to allocate funds to hold the poll, Chiweshe said.
It took the commission more than a month to announce results from the disputed March 29 presidential election.