Last week, Mr Trump praised North Korean leader Kim Jong Un for his "wise" decision while UN Secretary-General Antonio Guterres said he had told Russia, Japan, the United States, China and North and South Korea that he was available to help broker talks.
He said that military would "proceed more thoroughly" with the ongoing Ulchi Freedom Guardian exercise, a joint training drill between South Korea and the US that started Monday. It said earlier that the third missile appears to have blown up immediately.
The U.S. military's Pacific Command said it had detected three short-range ballistic missiles, fired over a 20 minute period.
Mr Tillerson's latest remarks came just after the United States announced new North Korea-related sanctions targeting Chinese and Russian firms and individuals for supporting Pyongyang's weapons programs.
"Although the launches were no threat to Guam, it reminds us that we can not be complacent", Charfauros said.
North Korea's state media reported on Saturday that Kim had guided a contest of amphibious landing and aerial strike by its army against targets modelled after South Korean islands near the sea border on the west coast.
Tillerson had said he hoped that the lack of missiles launches or other "provocative acts" by Pyongyang could mean a path could be opening for dialogue "sometime in the near future". USA officials say none of the missiles posed any threat to North America at any point.
Solid fuel missiles are faster and easier to deploy, and harder to catch before they launch because there's a lot less to be done in terms of launch preparation.
Last month, it carried out two successful intercontinental ballistic missile (ICBM) launches, overseen by Mr Kim and apparently bringing the United States into range for the first time.
"They could be ballistic missiles but they could be rockets".
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