Rubio will use the trip to discuss energy cooperation and bilateral issues, including NATO commitments, the State Department said in an announcement last week.
"These are countries that are very strong with us, very cooperative with the United States, work very closely with us," Rubio told reporters before departing for Europe on Thursday.
Rubio, who in his dual role also serves as Trump's national security adviser, met Slovak President Peter Pellegrini on Sunday on his arrival in Bratislava and discussed energy and defence.
"An important topic of the talks was... defence cooperation and the fulfilment of commitments arising from NATO summits," Pellegrini's office said in a statement.
Rubio later met Slovak Prime Minister Robert Fico, who visited Trump in Florida last month.
The US diplomat's trip follows his attendance at the Munich Security Conference over the last few days.
On Monday, Rubio is expected to meet Hungarian leader Viktor Orban, who is trailing in most polls ahead of an election in April when he could be voted out of power.
"President (Trump) said he's very supportive of him, and so are we," Rubio said ahead of his trip.
"But obviously,, we were going to do that visit as a bilateral visit."
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 families and Christian conservatism.
Budapest has repeatedly hosted Conservative Political Action Conference events, which bring together conservative activists and leaders, with another due in March.
Both Fico and Orban have clashed with EU institutions over probes into backsliding on democratic rules.
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.
Even as other European Union countries have 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, but did not give any details.
Fico, who has described the European Union as an institution that is in "deep crisis", has showered Trump with praise, saying he would bring peace back to Europe.
But Fico criticised the US capture of Venezuelan President Nicolas Maduro in early January.
Hungary and Slovakia have also so far diverged from Trump's request for all NATO members to significantly increase their military spending to five per cent of GDP, and have raised defence spending to NATO's minimum threshold of two per cent, a lower level than some other NATO members.
On nuclear cooperation, Slovakia signed an agreement with the United States last month.
Fico has said US-based Westinghouse was likely to build a new nuclear power plant.
He is also interested in buying another four F-16 fighter jets from the US.
