Dominic Raab said the election is still "too close to call" but that he is totally confident the American system "will give us a definitive result", SKY news reported.
"The UK-US relationship is in great shape and we're confident that it will go from strength to strength, whichever candidate wins the election," he added.
Votes are still being counted, but Donald Trump has accused his opponents of "fraud on the American public" - and claimed victory in the US election before all results have been announced.
It could be days yet before the world knows who has won.
ZZ/PR