Benjamin Cruz, Guam Legislature Speaker, said the president’s rhetoric was contributing to escalating tensions between the United States and rogue nation.
Mr Trump has warned North Korea it will be “met with fire and fury” if the rogue state continues to threaten the US.
Asked if Washington was doing enough to de-escalate the North Korean crisis, Mr Cruz said he welcomed Rex Tillerson’s comments that appeared to add more calm to the situation.
The US Secretary of State said there was no sign the threat level from North Korea had changed and that Americans should “sleep well at night”.
Speaking on DW News, he said: “Unfortunately not. I liked Secretary Tillerson’s statement last night, that was probably the most responsible statement made by anybody from the United States in recent days.
“The statements made by Senator Graham and by the President himself are really irresponsible.”
North Korea has threatened to fire four missiles towards the US territory of Guam as the war of words with Donald Trump edges ever-closer towards all-out conflict.
The hermit state announced will launch the strike in mid-August, with military officials preparing the final details of the attack before seeking approval from despot Kim Jong-un.
President Donald Trump pledged yesterday to respond to North Korea’s threats with “fire and fury the likes of which the world has never seen” – a move which was immediately undermined by North Korea’s declaration of war.
But Kim Jong-un’s state media said the comments were “a load of nonsense” and claimed only “absolute force can work on him”, ratcheting up tensions and leading to fears the world may be witnessing the early days of World War 3.