The Defence Secretary said the UK was working "extremely closely" with the White House to bring about a diplomatic solution to the situation, despite President Trump warning of "fire and fury" if Kim Jong-Un's regime continues to test inter-continental ballistic missiles.
Appearing on the BBC's Andrew Marr Show, Mr Fallon said: "We're doing now what we can to bring about a diplomatic solution. What we have to avoid at all costs is this spilling over into any kind of military conflict, so we're working flat out at the UN to get a better resolution there, to enforce the existing sanctions, we're looking at sanctions across the EU and of course we're trying to persuade China to keep its neighbour in check.
And he made clear that the UK should take the North Korean threat seriously, given that Europe is nearer the Stalinist state than the continental US.
Mr Fallon said: "I'm very concerned at the situation in the Pacific, the US is fully entitled to defend its own territory, to defend its bases and to look after its people. But this involves us, London is closer to North Korea and its missiles than Los Angeles."
At the same time he acknowledged that the North Koreans do not yet have the capability to launch a missile as far as the UK.
He said: "Not yet, but they are clearly accelerating their missile programme, the range is getting longer and longer and we have to get this programme halted because the dangers now of miscalculation, of some accident triggering a response are extremely great.
"So, we've got to work at this problem and bring about a diplomatic solution that stops the development of North Korea's nuclear programme and enforces the sanctions we have at the moment."