Hugo Chavez made his remarks in Havana on Friday where he received a UN prize handed over by Fidel Castro, the president of Cuba.
His visit to Havana comes amid an intensifying war of words between Washington and Latin America's leaders.
Donald Rumsfeld compared Chavez to Adolf Hitler on Thursday and criticised Cuba and the populist leadership in Bolivia.
Chavez played down Rumsfeld's comparison.
"Let the dogs of the empire bark, that's their job," he said. "Ours is to battle to achieve the true liberation of our people."
Chavez said the US government was weakening already, and echoed Chinese revolutionary Mao Zedong's idea that capitalist countries were a "paper tiger" to be challenged.
"They are right to be worried, because they know what's happening here," Chavez said in a speech lasting nearly three hours after accepting his prize.
"They will forever try to preserve the US empire by all means, while we will do everything possible to shred it"
Hugo Chavez, the president of Venezuela
"They will forever try to preserve the US empire by all means, while we will do everything possible to shred it."
Rumsfeld expressed the same fears about Bolivia's new
reformist president, Evo Morales, whose election he described as "worrisome".
Addressing himself to Morales and the Bolivian people, Chavez said: "We will always be with you."
He praised all of Latin America's leftist leaders, from Brazil to Argentina to Chile, where a socialist, Michelle Bachelet, was recently elected president.
About 200,000 Cubans crowded Revolution Plaza for Friday night's ceremony granting Chavez Unesco's 2005 Jose Marti International Prize, which was presented by President Castro.
Thousands of young Venezuelans, Bolivians and other Latin Americans studying medicine free of charge in Cuba attended the ceremony, screaming their support for both leaders.
Castro also rejected Rumsfeld's comments, defending populism in his hour-long speech before Chavez took to the podium.
The Hitler comparison "is new and unexpected from those who,
like Hitler, dreamed of a 1,000-year empire", Castro said.
"Populist leaders are those who concern themselves with
their people, with health, with education"
Fidel Castro, the president of Cuba
"Populist leaders are those who concern themselves with More dangerous are those who possess dozens of thousands of nuclear weapons."
their people, with health, with education," he said. "
Earlier in the day, Jose Vicente Rangel, the Venezuelan vice-president also hit back, calling Bush "the North American Hitler" and comparing his administration to the Third Reich.
The Marti prize was created by Unesco in 1994 on the initiative of Cuba to recognise an individual or institution contributing to the unity and integration of countries of Latin America and the Caribbean.
It is awarded by Unesco on the recommendation of a seven-member international jury that includes Nadine Gordimer, the South African winner of the Nobel Prize for Literature.