Meeting Brazil's new right-wing President Jair Bolsonaro, an avowed opponent of socialism, Trump declined to predict a time-frame for the fall of Maduro, who has clung to power for nearly two months since the United States and Latin American powers declared him illegitimate.
"We haven't done the toughest sanctions," Trump told a joint news conference with Bolsonaro.
"We've done, I would say, right down the middle, but we can go a lot tougher if we need to do that," Trump said.
"What is happening there is a disgrace. This was one of the wealthiest countries in the world and all of a sudden, it is grief-stricken, poverty-stricken -- no food, no water, no air-conditioning, no anything," Trump said.
Trump renewed his call on Venezuelan security forces to desert Maduro, who still enjoys support from the leadership of the military.
"We call on members of the Venezuelan military to end their support for Maduro, who is really nothing more than a Cuban puppet," Trump said.
Bolsonaro, an outspoken foe of leftist ideology, said he had spoken to Trump about allowing the US military to position itself in Brazil near the Venezuelan border.
Trump has repeatedly said that "all options" are open on Venezuela, although Latin American and European allies have broadly warned against the use of force.
"Brazil will be more than willing and ready to fulfill this mission and take freedom and democracy to that country," Bolsonaro said.
Despite Trump's threats, the United States has already imposed a wide range of sanctions on Venezuela including the key step of cutting off the regime from revenue of its state oil company -- which counts on the United States as a key market through operator Citgo.
A sweeping embargo on Venezuela -- of the sort imposed for half a century by the United States against communist Cuba -- is seen as unlikely to gain wide support in Latin America, despite frustration with Maduro.