The brush-off came as two Venezuelan opposition leaders backed a US naval build-up near the South American country, calling it critical for the restoration of democracy.
Trump has dispatched eight warships and a submarine to the southern Caribbean in an anti-drug operation Venezuela fears could be the preamble to an invasion.
US forces have destroyed at least three suspected Venezuelan drug boats in recent weeks, killing over a dozen people.
On Sunday, the Venezuelan government released a letter that leftist Maduro had sent to Trump.
In the missive, Maduro -- whose July 2024 reelection was rejected as fraudulent by Venezuela's opposition and much of the international community -- 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 -- who during his first term tried unsuccessfully to expedite the Venezuelan president's ouster -- of trying to affect regime change.
It was "a first letter, I will certainly send them more," Maduro said Monday night during his weekly television program, during which he said his goal was "to defend the truth of Venezuela."
"If they close a door, you open a window, and if they close a window, you open a door with the truth of your country, lighting up the world, illuminating the White House with the light of the truth of Venezuela," he added.
Maduro's 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.
- 'Real and growing threat' -
Exiled presidential candidate Edmundo Gonzalez Urrutia, who the United States views as Venezuela's democratically-elected leader, said the military deployment was "a necessary measure to dismantle the criminal structure" he said Maduro leads.
Opposition figurehead Maria Corina Machado agreed, and said Venezuelan crime gangs were "a real and growing threat to the security and stability" of the Americas.
Maduro's claim to election victory last year sparked violent protests that were harshly repressed, leaving more than two dozen dead and hundreds behind bars.
The opposition said its own tally of results showed Gonzalez Urrutia, who stood in after the regime barred Machado from running, had defeated Maduro hands down.
Threatened with arrest, Gonzalez Urrutia fled to Spain. Machado remains in Venezuela, in hiding.
Another opposition figure, Henrique Capriles, last week came out against any US invasion.
"I continue to believe that the solution is not military, but political," the two-time presidential candidate said, adding Trump's actions were counterproductive and "entrenching those in power."
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