The Venezuelan government said overthrowing Maduro's regime would be "an unconstitutional change of government in the country, in open violation of the principles and purposes of the charter of the United Nations".
Almost 5,000 people leave Venezuela every day because of "instability and uncertainty" amid a crisis over the presidency and economy, and 3 million Venezuelans have already left the country since 2015, according to the UN's refugee agency.
An order by U.S. President Donald Trump to freeze the Venezuelan government's assets and cut off its funds is an act of "gross interference" and a violation of the norms of worldwide relations, China's foreign ministry said.
Bachelet said she was concerned businesses and financial institutions were "likely to err on the side of caution and completely halt transactions relating to the Government of Venezuela".
The new sanctions imposed by the USA administration is in a series of "arbitrary measures of economic terrorism against the Venezuelan people", the Foreign Affairs Ministry said, noting that Washington wants to "formalize its criminal economic, financial and trade embargoes".
She warned that the U.S. measures were likely to bring additional hardship to the Venezuelan people, who were already suffering from the effects of hyperinflation and a deep recession.
The Venezuelan government decided on Thursday to suspend talks with the opposition in response to the sanctions imposed by the United States.
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A video posted on social media showed dozens of people carrying yellow jerricans around the truck. Almost 80 people died in May in a similar incident near the airport of Niger's capital Niamey.
During the rally at the National Pantheon in Caracas, Diosdado Cabello, vice president of the PSUV party, condemned the sanctions, saying that the USA move against Venezuela "makes us more united and deepens our love for the country".
Bachelet did not blame one side or the other for the crisis inside Venezuela, but instead called on "all those with influence in Venezuela and in the global community to work together constructively for a political solution.by putting the interests and human rights of the long-suffering people of Venezuela above all else".
Venezuela is experiencing a political crisis that intensified in January after the US-backed opposition leader, Juan Guaido, proclaimed himself interim president.
In January, Guaido invoked the constitution to assume a rival interim presidency on the grounds that Maduro's 2018 re-election was fraudulent. "That way, the sanctions will be lifted tomorrow", he said.
While the order falls short of an outright trade embargo - notably, it spares Venezuela's still sizable private sector - it represents the most sweeping USA action to remove Maduro since the Trump administration recognized opposition leader Juan Guaido as Venezuela's rightful leader in January.
The US sanctions are meant to unseat Maduro's elected government.