Two sons of Panamanian ex-president
Ricardo Martinelli Linares and Luis Enrique Martinelli Linares said in a statement that news reports linking them to a $6 million payment aimed at securing substantial contracts for Odebrecht were "groundless."
Their father, who was president from 2009 to 2014, has been living in voluntary exile in Miami, Florida. Panama is seeking his extradition to face allegations of graft and spying on political opponents.
The brothers said they reserved the right to take legal action against those responsible for the alleged "media campaign" against them, adding that they could not allow their honor "to be tarnished by special interests."
Brazilian newspapers last week quoted former Odebrecht chief Luiz Eduardo Soares as telling Brazilian prosecutors that "commissions" had been paid to Martinelli's sons.
The US Justice Department recently reported that Odebrecht had paid bribes worth hundreds of millions of dollars to obtain contracts in nine Latin American countries.
It said the construction company paid more than $59 million in bribes to Panama between 2010 and 2014 to obtain contracts valued at $175 million.
Several members of Ricardo Martinelli's former cabinet have been jailed on related corruption charges.
Panama's government on Thursday warned of punishment for public employees who took bribes from Odebrecht.
That declaration came a day after US officials said Odebrecht and its petrochemical affiliate Braskem had agreed to pay $3.5 billion in "the largest-ever global foreign bribery resolution."
Odebrecht pleaded guilty to bribing government officials and political parties to the tune of $788 million to secure business on three continents -- mostly in Brazil, but also in 11 other countries in Latin America and Africa.