BRASILIA, May 27 (Reuters) - Shares in state-run oil company Petrobras fell on Friday after Brazilian President Jair Bolsonaro signaled a wide shake-up of the company's board and executive team amid rising dissatisfaction with high fuel prices.

Speaking to journalists outside a church in Brasilia late on Thursday, Bolsonaro said officials who had been at the company for more than six months could be considered unfit for further service, as they are wedded to the market-oriented policies that have squeezed Brazilians at the pump.

"I'm the majority shareholder. I have the right to propose, via the Mines and Energy Ministry, changes not only to the board of directors, but also to the executive board," he said.

"If they've stayed more than six months, they could have a policy of continuity regarding what has been happening over there."

Brazil-listed preferred shares in Petroleo Brasileiro SA , as the company is formally known, were off 2.8% in morning trade, underperforming the nation's benchmark Bovespa equities index, which was roughly flat.

Earlier this week, Bolsonaro announced he was ousting current Chief Executive José Mauro Coelho after only weeks on the job.

Since then, domestic media reports have indicated the shake-up at Petrobras could go beyond the CEO.

The right-wing leader has consistently decried high domestic fuel prices. The company, however, has maintained its current policy of pegging domestic rates to international prices.

As Petrobras does not have enough refining capacity to fulfill all of Brazil's needs, company leaders warn that significant and prolonged discounts could lead to shortages as private refiners and importers exit the market. (Reporting by Lisandra Paraguassu Writing by Gram Slattery Editing by Mark Potter)