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.

Thomas Anthony Carlin was dressed in uniform as he attended Belfast's Royal Courts of Justice again on Thursday.
He declined to apologise for his actions at an earlier hearing.
He also rejected an offer of legal representation and asked to have a jury decide on his behaviour towards Lord Justice Gillen.
But another judge refused his request, instead listing the case to be heard by him next week.
Mr Justice Horner said: "I'm going to arrange for a trial to take place on this issue of whether or not there has been contempt in the face of the court.
"I will hear it, there will not be a jury."
He also warned the policeman that, if found guilty, he could be fined or sent to prison.
Mr Carlin's alleged outburst came at the end of a ruling in a house repossession case in the High Court on Tuesday.
The 43-year-old had been representing himself in the legal battle with Santander bank over a property in County Antrim.
At the end of the hearing, he allegedly got up and moved towards the bench, claiming he was going to arrest Lord Justice Gillen.
Security and court staff intervened before he was led from the courtroom.
He was arrested on suspicion of two counts of common assault, but subsequently released without charge.
The Police Ombudsman was also notified.
Mr Carlin is alleged to have interrupted proceedings without justification, refused to resume his seat, approached the presiding judge, threatened to arrest him without lawful excuse and physically interfered with a court tipstaff.
He had been given until Thursday to secure a lawyer, apologise and provide an explanation for his behaviour.
But shortly after entering the courtroom again, Mr Carlin made his position clear.
He told Mr Justice Horner: "I believe for me to apologise to the court would be abandoning my defence."
The offer of legal assistance from a law firm that deals with the Police Federation was also turned down.
Mr Carlin further said: "I acted in my capacity as a police officer, I believed a crime had been committed (and) it was outrageous in nature.
"I believe the tipstaff and court staff who intervened... obstructed me in the execution of my duty."
At one stage Mr Justice Horner asked if he denied the alleged behaviour set out in writing.
"I completely dispute those facts," the officer replied.
The judge then cautioned him: "You realise that should you be found guilty of contempt in the face of the court you will be liable for a number of penalties including imprisonment."
Mr Carlin responded that he would comply with the findings of a jury.
However, he was told to turn up on Monday for a trial to be decided by Mr Justice Horner alone.
The South American trading bloc Mercosur has condemned President Trump for saying he was considering military action in the Venezuela crisis.
[NEXT_CONCEPT]
A policeman who allegedly approached one of Northern Ireland's most senior judges and threatened to arrest him is to go on trial for contempt of court.