The Constitutional Court ordered Mugabe two weeks ago to hold the poll by the end of July, following an application to the court by a Zimbabwean citizen demanding the president set a date before the current parliament expired.
Mugabe, who had anyway been pushing for an early vote, announced the election date on Thursday - fast-tracking changes to election laws by using a presidential decree to by-pass parliament.
A furious Tsvangirai, his partner in a fractious unity government, criticised him for complying with the court ruling rather than seeking an extension to the July 31 deadline.
The prime minister said Zimbabwe should hold the vote no earlier than Aug. 25 to allow for reforms of the media and security forces to ensure the poll was fair.
He said Mugabe, leader of the ZANU-PF party, was violating the constitution and a power-sharing agreement set up after bloody and disputed polls five years ago, by not consulting him before announcing the election date.
"President Mugabe has acted unlawfully and unconstitutionally and is deliberately creating and precipitating an unnecessary constitutional crisis," Tsvangirai told a news conference.
Justice Minister Patrick Chinamasa, of ZANU-PF, told foreign diplomats that it would have set a dangerous precedent if Mugabe had defied the court order. He also said a new constitution signed by the president last month regulated the conduct of security forces, and that Tsvangirai's demands had no merit.
He said the biggest issue for ZANU-PF was securing the removal of Western sanctions on Mugabe and his inner circle.
Zimbabwe is emerging from a decade of economic decline blamed on Mugabe and the political uncertainty has put a drag on a recovery. The economy probably contracted by up to 3 percent in the first quarter, according to Finance Minister Tendai Biti.
REGIONAL DIPLOMATS MEET
The president's poll announcement, two days before a meeting of the Southern African Development Community (SADC), is likely to infuriate regional diplomats trying to mediate between him and Tsvangirai's Movement for Democratic Change (MDC).
The SADC is desperate to avoid a repeat of the disputed 2008 poll, which prompted a flood of refugees into neighbouring countries after hundreds of people, most of them Tsvangirai supporters, were beaten and killed.
The regional group has asked Mugabe and Tsvangirai to agree on a roadmap towards elections. The meeting was also due to discuss how to find the estimated $132 million needed to fund the vote.
Lindiwe Zulu, South African President Jacob Zuma's top Zimbabwe negotiator, said she was flying to Harare on Friday but declined to comment on Mugabe's election announcement.
Tsvangirai and his MDC want to open up broadcast media, currently controlled by ZANU-PF, to all parties and to impose a code of conduct to stop the army and police meddling in the vote.
Tsvangirai said on Thursday he would not accept a situation in which Zimbabweans were "railroaded" into "another illegitimate election" and he would mount a legal challenge.
Mugabe was chairing a meeting of ZANU-PF's executive council on Thursday to agree on rules for its internal election of candidates, a process that has previously divided the party. The MDC will complete its own internal vote at the weekend.
Although there have been no formal opinion polls, surveys in the past year by Freedom House, a U.S. political think tank, and African research group Afro-Barometer have given Mugabe a narrow lead over Tsvangirai.
