The two held closed-door discussions after arriving in Panama for a summit.

Meanwhile, the US state department has reportedly recommended that Cuba be removed from its list of states said to sponsor terrorism.

Such a move could pave the way for the two countries re-opening embassies.

US President Barack Obama and Cuban leader Raul Castro are also due to hold their first formal meeting at the Summit of the Americas in Panama over the coming days.

Few details have emerged from the meeting between Mr Kerry and Mr Rodriguez. The last comparable high-level meeting was in 1959, when Fidel Castro met then Vice-President Richard Nixon.

Diplomatic ties froze two years later, but last year Mr Obama announced that a "new chapter" in relations would commence.

Meanwhile Senator Ben Cardin, a leading member of the Senate Foreign Affairs Committee, said the US State Department had recommended removing Cuba from the list of state sponsors of terrorism.

The move was "the result of a months-long technical review" and would be "an important step forward in our efforts to forge a more fruitful relationship with Cuba", he said.

Cuba is one of four countries still on the US list of countries accused of repeatedly supporting global terrorism; Iran, Sudan and Syria are others.

It was first put on the list in 1982 for offering sanctuary to militant ETA Basque separatists and Colombian Farc rebels.