The opposition has said that the move is an attempt by the government to buy time for a crackdown.
Initial parliamentary and presidential elections took place on March 29, with results not being released until May 2.
The opposition Movement for Democratic Change (MDC) won the parliamentary elections.
Tsvangirai also won the presidential election by 4.7 per cent. However, he did not gain 50 per cent of the vote required to become president without a second round.
George Chiweshe, the chairman of the Zimbabwe Electoral Commission, declined to confirm the extension.
However, he said that the authorities had approved a delay because they needed more than 21 days for their preparations.
The ruling party has claimed that the law provides for the postponement.
"Because we need more time for our preparations, to put our logistics together and the 21 days is insufficient."
A spokesman for the MDC said of the delay: "This is illegal and unfair.
"It is part of a programme to give Mugabe and Zanu-PF time to torment and continue a campaign of violence on the MDC."
Lovemore Madhuku, a constitutional lawyer and head of the National Constitutional Assembly pressure group fighting for a new constitution, said the delay was unlawful.
"It's unlawful under the electoral act... The act automatically sets the run-off date from the date of the first round.