"The consequences will be severe and they will be swift", Rubio said, also warning Maduro not to harm U.S. personnel working in the country, adding that the United States would also respond if aid workers were targeted.
Venezuela's government will distribute food to poor residents of the Colombian border city of Cucuta this weekend, the Information Minister said on Monday, an effort that would parallel opposition plans to bring in humanitarian aid.
U.S. President Donald Trump will say in a speech on Monday that Venezuela's military officials should "work toward democracy" or risk losing everything they have.
Maduro says the aid is unnecessary and illegal.
Previewing the speech, White House press secretary Sarah Sanders said Trump would express "strong support" for Guaidó, whom the U.S. recognizes as the country's rightful president, and condemn President Nicolás Maduro's government and its socialist policies. Mr. Trump has used Venezuela as an example of what, in the administration's view, happens when a country turns to socialism.
Food supplies, hygiene kits and nutritional supplements have been stockpiled near the Venezuelan border in Cucuta, Colombia.
Maduro, who has the backing of Russian Federation and China, has told the military, which remains loyal to him, not to let any convoys of aid cross into Venezuela.
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"If it doesn't enter on the twenty-third, it will enter on the twenty-fourth, it will enter on the twenty-fifth" of February, he said.
But it is unclear whether the military will allow aid to cross the border.
Mr Maduro, who denies the existence of a humanitarian crisis, dismisses the opposition moves as a "political show" and a cover for a U.S. invasion.
"Whoever prevents the entry of humanitarian aid is condemned to spend the rest of their lives fleeing global justice, because that is an worldwide crime", Mr Rubio said in Spanish.
An imploding economy has driven an estimated 2.3 Venezuelans to migrate, while those who remain have been punished by hyperinflation that has put scarce food and medicine out of reach for many.
Mr Maduro has dismissed the humanitarian assistance as "crumbs" and "rotten and contaminated food" while blaming shortages of food and medicine on United States sanctions.