In a nationally broadcast appearance hours after Trump spoke, Maduro said that talks had long been underway between high officials in his government and the U.S. administration.
"We've had secret meetings in secret places with secret people that nobody knows," Maduro said, adding that all talks had been carried out under his "direct" authorization. "Sure there's been contact and we'll continue having contact."
The Associated Press reported over the weekend that the U.S. has made secret contact with socialist party boss Diosdado Cabello as close allies of Maduro's inner circle seek guarantees they won't face prosecution for alleged abuses and crimes if they cede to growing demands to remove him.
Maduro did not name any officials in his government participating in U.S. meetings. The socialist leader said that he's ready to meet with Trump himself to normalize relations, an offer he's made before.
Venezuela was one of many topics addressed by Trump when he took questions from reporters earlier Tuesday during his meeting with Romanian President Klaus Iohannis.
Trump, however, refused to say whether such dialogue is being conducted with Cabello, considered the nation's second most powerful politician after Maduro.
The U.S. considers opposition leader Juan Guaidó to be the legitimate president of the country.
An administration official told AP the goal is not to prop up Cabello or pave the way for him to substitute Maduro, but to ratchet up pressure on the regime by contributing to the knife fight the U.S. believes is taking place behind the scenes among competing circles of power within the ruling party.
At a press conference Monday in Caracas, Cabello shied away from discussing any details of the meeting and at one point likened it to "a lie, a manipulation." But he also said he has long stood welcome to talk to anyone, so long as any discussions take place with Maduro's approval.
Talks sponsored by Norway between the opposition and government have been slow moving and were suspended this month by Maduro.
Trump repeated Tuesday that his government is helping Venezuela "as much as we can" so that the country resolves its political and financial crises, which he attributed to socialism.
"Fifteen years ago it was one of the wealthiest countries. Now it's one of the poorest countries," he said.
The U.N. estimates that at least four million Venezuelans have left their country because of hyperinflation and severe shortages of food and medicine.