More than 120 people have died in protest-linked incidents since April.
Peru has been a fierce critic of Mr Maduro's government.
"Whoever betrays the nation, whoever takes up arms against the FANB will receive exemplary punishment", he said, referring to Venezuela's armed forces.
Venezuela has been under constant attack from the Trump administration after the recent election of a National Constitutional Assembly charged with updating the country's constitution.
Assembly president and former Foreign Minister Delcy Rodriguez added in her tweets that "insults and aggressions" against Venezuelan President Nicolas Maduro would be rejected by the "anti-imperialist people of Venezuela".
Venezuela's new Constituent Assembly today strongly backed socialist President Nicolas Maduro in the face of the "vile threats" of his United States counterpart Donald Trump, who said United States military action was an option to quell the South American country's devastating crisis. Venezuela is not very far away and the people are suffering, and they are dying.
Earlier this week, the Trump administration imposed new sanctions on Venezuela, targeting members of the new all-powerful constituent assembly.
On Thursday, Trump claimed that action needed to be taken against Venezuela and declared that all options remain on the table, including a potential military intervention.
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Reuters reported later Friday that the Pentagon said the White House hadn't given it any orders on Venezuela.
"Mr. Donald Trump, here is my hand", Maduro said, adding that he wants as strong a relationship with the U.S.as he has with Russian Federation, according to The Associated Press.
The crisis has fueled the street demonstrations that have gripped Venezuela for the past four months.
South American trading bloc Mercosur has spoken against Mr. Trump's latest comments on the Venezuela situation.
Maduro attempted to begin dialogue with Washington and requested a phone call with Trump on Friday.
The US government has sanctioned more than 20 Venezuelan government officials in the last few weeks. "President Trump will gladly speak with the leader of Venezuela as soon as democracy is restored in that country", the White House responded in a statement.
Venezuelan President Nicolas Maduro stated that a new constitution would help resolve the nation's political standoff.
Not even the frustration over Trump's decision to partially roll back Obama's opening to Cuba - a diplomatic thaw that was applauded across the region's political spectrum - or his constant talk of building a border wall to keep out immigrants got in the way of presenting a united front toward Maduro.