Brexit Secretary David Davis said a future free trade agreement the UK seeks with the European Union is "massively important to both sides".
Mr Davis was speaking after meeting Slovak prime minister Robert Fico on Friday.
He said Britain exports goods worth 230 billion euro (£200 billion) to the EU while EU nations export goods worth 290 billion euro (£250 billion) to the UK.
Mr Davis said a recent investment of Jaguar Land Rover in Slovakia is "a component of that co-process... we want to preserve, enlarge and encourage".
He also said the Government wants to assure Slovak citizens in Britain "they will have equally good arrangements in the future as they have now".