Mexico has resisted allowing foreign governments to bring cases in its courts, contending that this might infringe on Mexican sovereignty.
A right-leaning paper accused the US of violating Mexican sovereignty.
He characterized the proposals as outrageous encroachments on Mexican sovereignty.
With Mexico's presidential election campaign in full swing, candidates are also under pressure to reject the American action as an incursion on Mexican sovereignty.
"We have the utmost respect for Mexican sovereignty," said a statement from the State Department.
Opposition lawmakers, especially from the Institutional Revolutionary Party, tend to see any attempt to open Mexico's protected energy industry as an assault on Mexican sovereignty.
Local television reporters asked Mr. Madrazo whether he had ceded Mexican sovereignty to the United States.
He could not give in to the violation of Mexican legal sovereignty and provoke the animosity of many relatively independent revolutionary warlords in Mexico's regions.
But holding the loan guarantees hostage to them flagrantly offends Mexican sovereignty.
Yet even if there had been sufficient evidence, the abduction clearly violated Mexican sovereignty.