BRASILIA, March 13 (Reuters) - The fallout from a missing Petrobras dividend may have shifted the balance in a tug-of-war between the CEO of the state-run firm and the energy minister holding sway over its board.

Chief Executive Jean Paul Prates saw his proposal for an extraordinary dividend, widely expected by shareholders, go down in flames last Thursday, blocked by government-appointed board members. The next day Petrobras shares plunged more than 10%.

The episode rang alarm bells in the market about political risks for Latin America's largest oil company, which was saddled with heavy debts, unproductive investments and graft scandals when President Luiz Inacio Lula da Silva's Workers Party last held power a decade ago.

Prates had warned Lula in a meeting earlier last week that withholding the dividend would be a disaster, battering the trust of minority shareholders, people familiar with the matter told Reuters.

But Mines and Energy Minister Alexandre Silveira, who exerts influence through the Petrobras board, convinced Lula in that meeting last week that Petrobras should hold onto cash in order to ramp up investments, the sources said. They said Lula's chief of staff, Rui Costa, was also sympathetic to Silveira's view.

Petrobras, Lula's press office and the Mines and Energy Ministry did not respond to requests for comment.

Although Lula picked Prates personally for the Petrobras job, and their relationship has withstood a rocky first year, the CEO could tell he was outgunned. Over the weekend, he reached out to Finance Minister Fernando Haddad, seeking to "counterbalance" the pressure from Silveira and Costa, according to one of the sources, who spoke on condition of anonymity.

Lula's confidence in Haddad has helped the finance minister pass new budget rules and battle for fiscal discipline despite friendly fire from the leftist president's political base. A hefty dividend payment to the government, the biggest Petrobras shareholder, would also help balance the federal budget.

When Lula, Prates and Silveira met again on Monday to discuss plans for Petrobras, Haddad was in the meeting. Afterwards, both Haddad and Silveira echoed the CEO's assurances that cash set aside from last year's profit would eventually be used for shareholder dividends.

Perhaps more importantly, Silveira said Haddad would appoint a Petrobras board member at a shareholder meeting next month, diluting the energy minister's sway on the board.

Haddad plans to appoint Rafael Dubeux to the board seat, two sources told Reuters, tapping a senior Finance Ministry official responsible for a program to drive investment in sustainable development.

The move marks a reversal from last month, when sources said the government was planning to reappoint its six board members at Petrobras, in a sign of Silveira's continued influence.

The energy minister has been a vocal critic of Petrobras management under Prates, blasting what he calls high fuel prices and underwhelming investment plans.

Those broadsides have aligned often with Lula's own rhetoric about the state-run oil firm, which he has criticized for paying excessive dividends under the previous government.

Lula called again in a TV interview on Monday for Petrobras to pay smaller dividends to shareholders and invest more in projects that help all Brazilians.

Still, with Haddad in his corner, Prates may find it easier to carry the day in future debates at the presidential palace - and on the Petrobras board.

"Until last week, it seemed Prates was hanging by a thread. But the scenario has changed - he's holding on," said one government source. (Reporting by Lisandra Paraguassu in Brasilia and Rodrigo Viga Gaier in Rio de Janeiro; Additional reporting by Marta Nogueira and Fabio Teixeira; Editing by Brad Haynes and Jonathan Oatis)