By Anthony Boadle

BRASILIA (Reuters) - Major parties in Brazil's governing coalition pressed the Supreme Court on Friday to overturn a Senate decision allowing former President Dilma Rousseff to remain politically active after her dismissal in an impeachment trial this week.

The Senate voted on Wednesday to remove Rousseff from office for manipulating the federal budget to hide the real state of Brazil's ailing economy in the run-up to her 2014 re-election.

In an unexpected separate vote, lawmakers spared the leftist leader from an eight-year ban on running for public office or holding any position in government, as provided for in Brazil's constitution.

"They did a last-minute legal trick and guaranteed the former president's political rights," Senator Jose Medeiros, of the Social Democratic Party, said on Friday. He spoke after filing a request to annul the second vote, which he said was unconstitutional.

His motion was joined by another from the Democrats party and the Brazilian Social Democracy Party, two heavyweights in the coalition assembled by the new President Michel Temer, following a similar motion by Green Party Senator Alvaro Dias on Thursday.

The head of the ruling Brazilian Democratic Movement Party, Romero Juca, also condemned on Twitter the Senate's vote separating the matter of Rousseff's ouster from her future political life.

Rousseff told a news conference that senators had voted for her to retain her political rights because they were undecided over whether charges she doctored official budget figures warranted her dismissal.

Rousseff, who has denied any wrongdoing, said she had no plans to run for elected office but would remain politically active in opposition to what she called the "illegitimate" government of her conservative former vice president.

"My political plan is to oppose this government," she said.

Rousseff's lawyer Jose Eduardo Cardozo said the attempt to deprive her of political rights will fail because the Supreme Court would have to annul both votes in the Senate since one had influenced the other.

Temer, initially annoyed by the vote to maintain Rousseff's rights, played down the twist in her final removal on Friday.

"The Senate made that decision, wrongly or rightly, but the Senate made that decision," Temer said on the sidelines of a business summit in Shanghai ahead of a G20 summit in China.

Rousseff herself appealed to the Supreme Court on Thursday to annul the decision to oust her, a request that is unlikely to succeed.

(Reporting by Anthony Boadle; Editing by Tom Brown)