Trump told reporters that he would not rule out a "possible military option" in Venezuela, which has long grappled with political and economic crisis.
Venezuela's Defense Minister Vladimir Padrino told state television on Friday that Trump's threat was "an act of craziness".
Even for a confirmed Trumpian, the president's statement yesterday that "A military operation and military option is certainly something that we could pursue" in Venezuela is perplexing. You know we're all over the world, and we have troops all over the world, some that are very, very far away. "Venezuela is not far away", Trump said, referring to the close proximity of the country in Latin America.
Diplomacy between the two got off to a shaky start, with the White House saying that, although Mr Maduro had requested a phone conversation with Mr Trump, the latter would gladly speak with him when democracy is restored.
Weeks ago the USA imposed sanctions on Maduro, terming him a dictator.
Maduro hasn't made the same kind of threats toward the USA or its allies like North Korean leader Kim Jong-un has.
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A week ago, Trump's top national security adviser H. R. McMaster said in a TV show that he did not see a military intervention from any outside source as likely.
Trump said Friday that he had not ruled out possible military action in Venezuela in response to growing political and social turmoil in the country.
The country has been the scene of deadly protests against Maduro's government for the last four months. On Friday Peru expelled Venezuela's ambassador after Caracas sent an "unacceptable" response to regional condemnation of its new constituent assembly.
The Socialist leader, with his country starving due to poor government policies and a bottoming out oil market is facing more and more pressure as he cracks down on opposition leaders, has reached out to the man he called a crass imperial magnate and blasts for USA sanctions against officials in his socialist administration. "I am sure that we will all be on the front lines of defending the interests and sovereignty of this beloved Venezuela", he added.
The 545-member assembly, which has the rights to amend the constitution and reorganize the government, "aims to fix the malfunction" plaguing the country's governing system, according to Delcy Rodriguez, the recently elected president of the new legislative body.