In Slovakia, which, like Hungary, relies on Russian oil and gas and has uneasy relations with the rest of the European Union, Rubio discussed energy and defence with Prime Minister Robert Fico and President Peter Pellegrini.
It was the first visit in seven years by a US secretary of state to the country of 5.5 million people that borders Ukraine.
"Under President Trump, this administration is going to make not just Slovakia but central Europe a key component of how we engage the continent and the world," Rubio said.
On Saturday, Rubio, who is also Trump's national security adviser, delivered a message of unity at the Munich Security Conference while maintaining the administration's criticism of Europe following a scarring year for Transatlantic ties.
Trump's criticism of Europe, imposition of tariffs on EU countries and his ambition to acquire Greenland from fellow NATO Denmark have prompted western European leaders to increasingly look at carving an independent path.
"We expect every country in the world to act in their national interest. That is what countries are supposed to do," Rubio said.
"When our national interests are aligned ... this is an extraordinary opportunity for cooperation and partnership."
Fico, who has said the European Union is in "deep crisis", visited Trump last month in Florida and showered the Republican president with praise, saying he would bring peace.
Both Fico and Hungarian Prime Minister Viktor Orban, whom Rubio will meet on Monday in the second leg of his trip, have been accused by EU institutions of weakening the judiciary, media and anti-corruption enforcement.
They have also maintained ties with Moscow, criticised and at times delayed the imposition of EU sanctions on Russia and opposed sending military aid to Ukraine.
In remarks before departing Washington on Thursday, Rubio said Trump is very supportive of Orban, who is trailing in most polls ahead of an election in April when he could be voted out of power.
Orban, one of Trump's closest allies in Europe, is considered by many on the American hard-right as a model for the US president's tough policies on immigration and support for Christian conservatism.
Budapest has repeatedly hosted Conservative Political Action Conference events, which bring together conservative activists and leaders, with another due in March.
While other European Union countries secured alternative energy supplies after Moscow invaded Ukraine in 2022, including by buying US natural gas, Slovakia and Hungary have continued to buy Russian gas and oil, a practice the US has criticised. Rubio said this would be discussed during his brief tour.
On nuclear cooperation, Slovakia signed an agreement with the United States last month.
Fico said he hoped an agreement with US-based Westinghouse could be signed by next year that would lead to a consortium that will build a new nuclear power plant in Slovakia by 2040.
He added that Slovakia wants to buy four more F-16 fighter jets.
Hungary and Slovakia have raised defence spending to NATO's minimum threshold of two per cent rather than the five per cent of GDP requested of all NATO members by Trump.
Fico said Bratislava was aware it needed to raise its military capabilities and was working on it.
Fico has diverged from Washington in one area, when he criticised the US capture of Venezuelan President Nicolas Maduro in early January.
When asked about the issue at the news conference, Rubio shrugged off the difference of opinion.
"A lot of countries didn't like what we did in Venezuela. That's okay. That was in our national interest ... So what? That doesn't mean we're not going to be friends," Rubio said.
