Argentina said dialogue and diplomacy were the only ways to promote democracy in Venezuela.
Venezuela's foreign minister said Mr Trump's words had been hostile and disrespectful and risked destablising Latin America.
Violent demonstrations since April have left more than 120 people dead.
President Nicolas Maduro's new constituent assembly - which can rewrite the constitution and could override the opposition-controlled parliament - has been widely criticised as anti-democratic.
Mercosur - which includes the region's largest economies Argentina and Brazil as well as Paraguay and Uruguay - indefinitely suspended Venezuela's membership last week.
Other Latin American countries also condemned Mr Trump's comments, including Mexico, Colombia and Peru, which said Mr Trump's threat was against UN principles.
Peru has been a fierce critic of Mr Maduro's government. On Friday Peru expelled Venezuela's ambassador after Caracas sent an "unacceptable" response to regional condemnation of its new constituent assembly.
Peruvian President Pedro Pablo Kuczynski has urged Mr Maduro to resign and called him a dictator.
On Friday evening Mr Trump told reporters the US had "many options for Venezuela, including a possible military option if necessary".
"The people are suffering and they're dying," he added.
The US recently imposed sanctions on President Maduro, branding him a dictator.
The White House later said that Mr Maduro had requested a phone call with the American president.
In response, the White House said Mr Trump would gladly speak to his Venezuelan counterpart, when democracy had been restored in the country.
The Venezuelan opposition accuses Mr Maduro of trying to cling on to power, but he says the new assembly will bring peace to the country.
The South American trading bloc Mercosur has condemned President Trump for saying he was considering military action in the Venezuela crisis.