A long-running investigation into corruption at Brazil's state-run oil company has moved a step closer to President Dilma Rousseff: Police have ordered the arrest of the political marketing expert who helped her win two elections.

In a televised news conference on Monday, police accused Joao Santana and his wife, Monica Moura, of receiving $3 million in illicit funds from offshore companies controlled by Odebrecht, a major construction company under investigation for its relationship with the state-run oil company Petrobras.

Odebrecht's president, Marcelo Odebrecht, has been detained since June last year, accused of corruption and money-laundering.

The arrest warrants are part of the two-year-long Operation Car Wash, an investigation into kickbacks at Petrobras that has implicated dozens of senior politicians and some of the country's top business leaders.

Santana and Moura have been in the Dominican Republic working on the re-election campaign of President Danilo Medina. The campaign said Monday that Santana submitted his resignation as an adviser. According to their lawyer, they are willing to cooperate with any police inquiry.

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As well as masterminding Rousseff's 2010 and 2014 election victories, Santana also ran former president Lula da Silva's successful 2006 campaign.

The arrest order is a new blow to the Rousseff administration. The president is currently battling an impeachment process over allegations that her administration used state-run banks to fill budget gaps. But she also faces separate charges at the country top electoral court, where the opposition has accused her of using illicit funds to finance her re-election campaign.

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