LIMA, March 11 (Reuters) - Peru's presidential frontrunner Keiko Fujimori would work to push out new mines faster if elected, but only for companies that have community backing, her economic adviser said on Friday.

Jose Chlimper, who is also the center-right politician's running mate, said Newmont Mining Corp and Southern Copper Corp did not do enough to build local support for their proposed mines Conga and Tia Maria.

The companies, which suspended the projects because of local protests, had revised their plans to ease worries about environmental impacts and are investing in social programs.

"They have to look at their community relations plans and win back the legitimacy that they lack today," Chlimper said in an interview with Reuters.

"We're going to support the effort of serious companies to make big projects viable, but the ones that have not acted properly will not have our support," he said.

Peru's next president will likely inherit an economic recovery driven by surging copper output from new mines, but no major projects are set to come on line in coming years.

Chlimper said center-right Fujimori would create a legal framework to help miners turn local communities into shareholders in their projects - a tool to build support for new mines that some companies in Peru have already implemented.

Fujimori, the daughter of imprisoned ex-president Alberto Fujimori, has railed against President Ollanta Humala for fanning anti-mining sentiment as a candidate. Humala narrowly defeated her in her first presidential bid in 2011.

This year's race has been shaken by the electoral board's disqualification of two leading candidates a month before the April 10 vote. Fujimori's closest rival, Julio Guzman, was barred because his party did not comply with electoral procedures - a decision he calls "fraud" that threatens to tarnish the legitimacy of the next president.

Peru is set to become the world's second biggest copper supplier, but concerns about the impacts of mining near farming communities threaten to hurt new investments. Fujimori has pledged stiff fines for miners that pollute as she seeks votes on a populist platform in Andean regions.

Chlimper said Fujimori would study whether the corporate tax rate that Humala lowered as growth slowed had helped draw investments. The rate will gradually slide to 26 percent in 2019 from 30 percent in 2014.

"We'll revise it according to its results," Chlimper said.

But he added that her government would mainly aim to boost slumping revenues by implementing policies that expand the tax base.

(Reporting By Teresa Cespedes, Writing by Mitra Taj; Editing by Bernard Orr)