By Dana Ford

LIMA, Oct 17 (Reuters) - Peru's new prime minister, worried the opposition will call disruptive strikes, pleaded on Friday with the country's two leading leftists for a truce as he tries to bring the benefits of an economic boom to the poor.

Yehude Simon -- himself a leftist who now supports private investment -- wants to avoid the marches, rallies and walkouts that plagued his predecessor, who stepped down last week in a corruption scandal.

Ollanta Humala, an ultra-nationalist, and Mario Huaman, head of Peru's largest labor organization, have backed dozens of rallies this year to demand the poor get a bigger share of growth. They say they are tired of waiting for change.

Simon, whose cabinet is preparing for the APEC summit next month in Peru, appealed to them both for calm.

"We will not permit damage to public and private property, much less road blocks," Simon said.

Humala, who plans to run for president in 2011, when Simon might also be a candidate, agreed to cooperate, at least for the moment.

"We can give him the benefit of the doubt, but not a blank check," he told reporters after meeting the prime minister.

Simon, who has evolved into a pragmatist since being imprisoned in the 1990s over ties to an armed guerrilla group, was the governor of a northern province in Peru.

Critics on the left accuse him of abandoning his ideology and becoming too mainstream.

President Alan Garcia, a centrist whose approval rating has tanked to 19 percent, hired Simon this week in a broad cabinet reshuffle aimed at stemming a corruption scandal that involved rigged auctions for petroleum concessions.

Garcia has said Simon will bring focus to social programs aimed at lowering the poverty rate from 40 percent. But Huaman has his doubts.

"We hope you do not forget where you came from and the promises you made," Huaman told Simon at a press conference. (Editing by Anthony Boadle)

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