Calls within the Brazilian Democratic Movement Party to ditch the leftist leader's coalition have been growing as Rousseff faces a bruising recession, a spiraling corruption scandal and a probe of alleged electoral violations, as well as possible impeachment.
The huge centrist party, known as the PMDB, is seen as a kingmaker in Brazil, and losing its backing would be a devastating blow for the country's first woman president.
PMDB lawmaker Osmar Terra, one of the leaders of the movement to break with Rousseff and her Workers' Party (PT), said the president has "lost control" of Latin America's largest country, which is stuck in what may be a record recession even as it prepares to host the Olympics in Rio de Janeiro in August.
"The PT and the government are over."
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The decision was taken at the PMDB's national convention in Brasilia, which came ahead of nationwide protests Sunday calling for Rousseff's impeachment.
There was vocal hostility to Rousseff at the convention, with many members shouting "Down with Dilma!" in between speeches.
Party leaders said that during the 30-day period, PMDB members will be barred from accepting positions in Rousseff's administration to prevent her from interfering in the final decision.
Among the issues at stake in the internal debate is whether PMDB lawmakers will be free to decide how to vote if Congress opens impeachment proceedings against the president.
Temer sought to downplay the calls for a break, though he also played to the anti-Rousseff crowd.
"We can't ignore the fact that the country is going through an extremely serious political and economic crisis. But this is not the time to divide Brazilians," he said.
Congress is mulling impeachment over allegations Rousseff fudged the government's accounts to boost public spending during her 2014 re-election campaign and hide the magnitude of the recession racking the once-booming South American giant.
Meanwhile, the Supreme Electoral Court is considering a case that could result in judges invalidating Rousseff's re-election.