Tsvangirai said over the weekend that he would participate in the run-off but added that failure to hold the second round within the time limit risked rendering the election process illegitimate.
Government officials say the electoral commission has up to a year to hold the second round.
"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.
Tsvangirai, leader of the opposition Movement for Democratic Change (MDC), maintains that he won the first round and says that the official figures were fraudulent.
But Tsvangirai, who has remained abroad since the vote because of threats to his life, said on Saturday from South Africa that he will take the risk of returning to Zimbabwe to contest a run-off, despite the danger.
Mugabe has been accused of orchestrating violence against the opposition since the first round, raising questions about whether a run-ff would be free or fair.
The opposition accuses the electoral commission of being biased towards Mugabe and says any further delays could see more activists come under attack in an effort to prevent them voting.
Meanwhile, Mugabe's ruling Zanu-PF party has launched its run-off campaign.
Patrick Chinamasa, a presidential spokesman, said on Sunday that the party will not allow an opposition victory.
"Mugabe, at 84, do you believe he is fighting for himself? That's what the people of Zimbabwe should understand," he told reporters in Harare.
"He is fighting blatant attempts at recolonising Zimbabwe."
Tsvangirai has told regional leaders that if he were to win the presidency, he would respect Mugabe's place in Zimbabwe's history.
Tsvangirai told reporters on Saturday that Mugabe would be treated as the "father of the nation" in the interest of building peace and stability in Zimbabwe.
Last month he said he believed that the Zimbabwean people would press for Mugabe to stand trial for crimes against humanity.