Trump told reporters that he would not rule out a "possible military option" in Venezuela, which has long grappled with political and economic crisis.
The Pentagon later said the USA military had not received any orders on Venezuela from the White House.
"We had some very good meetings, some very good ideas, very good thoughts, and a lot of decisions were made", Trump said following the briefing, without providing details.
In response to Maduro's actions, Peru has ordered the expulsion of the Venezuelan ambassador from Lima.
The Pentagon quickly responded that it has not received any special orders from Trump regarding the South American country.
President Nicolas Maduro has been under intense criticism around the world for installing a new all-powerful assembly that supersedes the Venezuelan congress and is packed with Maduro loyalists. Maduro has been called a dictator by U.S. leaders as well as some of his own people.
Venezuela's foreign ministry is expected to issue a formal response to Trump's threat by way of a statement later on Friday.
The political crisis in Venezuela appears to grow more volatile.
The Trump administration, along with many other countries, has been critical of Venezuelan President Nicolás Maduro and his creation of a new constituent assembly.
Elias Jaua, head of the Presidential Commission for the National Constituent Assembly, said that the ANC did not need the recognition of "any government".
The new body has the ability to rewrite the constitution and could override the opposition-controlled parliament, the National Assembly. Needless to say, the Venezuelan leader who was in dire straits just got a shot in the arm from the USA president.
Violent demonstrations since April have left more than 120 people dead.
Although Venezuela has the world's largest proven oil reserves, its economy has collapsed in recent years as the country led first by the late Hugo Chávez and then by his successor, Maduro, has resorted to increasingly authoritarian measures to consolidate power.