On Sunday, the Venezuelan government released a letter that leftist Maduro had sent to Trump.
In the missive, Maduro rejected as "absolutely false" US allegations that he leads a drug cartel and urged Trump to "keep the peace."
Reacting on Monday, White House Press Secretary Karoline Leavitt said Maduro's letter contained "a lot of lies."
She added the Trump administration's position on Venezuela "has not changed" and it viewed the regime as "illegitimate."
The US deployment is the biggest in the Caribbean in years.
Maduro has accused Trump of trying to affect regime change.
His defense minister, Vladimir Padrino Lopez, last week accused the United States of waging "an undeclared war" in the Caribbean, underlining that occupants of alleged drug boats were "executed without the right to a defense."
Thousands of Venezuelans have joined a civilian militia in response to Maduro's call for bolstering the cash-strapped country's defenses.
Some Venezuelans have welcomed the US actions, however, hoping they hasten Maduro's downfall.
RHM/
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