UPDATE 2-Peru's Humala makes concessions in election plan

* Rules out contentious pension, tax changes
* Steps up attacks on rival as lead slips
* Humala has been dogged by 'double-talk'

By Patricia Velez and Caroline Stauffer

LIMA, May 13 (Reuters) - Leftist presidential candidate Ollanta Humala, trying to woo moderate voters, scrapped a plan to nationalize Peru's private pension funds and vowed to respect an independent Congress and judiciary if elected.

In his updated election platform released on Friday, Humala promised to leave the private pension system untouched instead of replacing it with a government-run system.

Humala, a former army officer who has tempered his radical image since narrowly losing the 2006 election, also dropped plans to raise the corporate income tax rate on firms in the country's vast mining sector to 45 percent from 30 percent.

But he still plans to slap a windfall profits tax on mining companies that he said would raise $1-$2.5 billion a year in revenue to help fight poverty that afflicts a third of the population.

The revision of his controversial plan -- it is the second time he has changed it during the campaign -- seeks to calm Peruvian voters and investors worried that he will intervene in the fast-growing economy. Those concerns eroded his lead and this week he fell behind right-wing rival Keiko Fujimori in two opinion polls three weeks away from the June 5 run-off.

"Our main goal is to make sure that economic growth benefits everyone, beginning with the poorest," Humala told reporters. "We want the country to believe that, with God, we can start a great transformation that will be gradual but consistent, without destabilizing change."

Humala has increasingly sought to recast himself as a moderate like Brazil's popular former President Luiz Inacio Lula da Silva, who abandoned his hardline politics to capture the political center when he was first elected in 2002.

Humala's recent overtures have helped win him new supporters, but critics had said his more conciliatory public image still clashes with angry rhetoric in his government plan, which rails against free-market economic policies and multinational corporations. Those discrepancies led to charges he was engaging in "double-talk" and could not be trusted.

Critics have said that reforms Humala proposed in his original campaign platform would have undermined judicial independence, while memories of Congress being shut in 1992 by jailed former President Alberto Fujimori still unnerve voters concerned about the strength of Peru's democracy.

Humala's revised plan reiterated earlier pledges to respect the Central Bank's independence, run a balanced budget, honor Peru's foreign trade pacts and only serve one term.

His detractors had voiced concerns that he might try to change the constitution to allow him to run for any number of consecutive terms, like his former political mentor, Venezuelan President Hugo Chavez.

Humala won the first round presidential vote on April 10 but is now narrowly trailing Fujimori, a lawmaker and daughter of the former president, who is favored by the business community.

Her father's government opened the economy and slayed hyperinflation but collapsed in 2000 in a cloud of corruption and human rights scandals stemming from his crackdown on insurgents.

Like Humala, she has also said Peru should introduce a windfall profits tax on miners to fund social programs.

Humala, who for months avoided directly criticizing Fujimori, has in recent days sought to discredit her presidential bid with sharp attacks.

"The option we offer today to Peru is the road toward a democratic and conciliatory government, instead of one of continued corrupt power that only serves elites -- tied to corruption and the return of Fujimori's authoritarianism."

Writing by Terry Wade; editing by Anthony Boadle