The alert comes just days after a false cellphone alert warning of an incoming ballistic missile terrified residents in Hawaii.
Saudi-led coalition blames Iran for supporting Houthi rebels in Yemen, after the kingdom's air defences intercepted a ballistic missile over the southern part of Saudi Arabia on Friday.
Washington's new diplomatic overture comes after Pyongyang said it had successfully tested an advanced intercontinental ballistic missile.
Hawaii State Governor David Ige said the new siren test will ensure the public knows what they should do in case of an imminent attack days after North Korea fired a powerful nuclear-capable intercontinental ballistic missile.
The DPRK fired its highest-ever intercontinental ballistic missile reaching an altitude of 4,475 kilometres (2,781 miles).
The announcement, though planned weeks earlier, came hours after North Korea tested an intercontinental ballistic missile, which flew about 1,000 kilometers before landing in the Sea of Japan.
The US president made the request as his Asia tour moved on to South Korea, a key ally in the struggle with nuclear-armed North Korea.
State television carried footage of the launch of the Khoramshahr missile, which was first displayed at a high-profile military parade in Tehran on Friday.
China, Pyongyang's main economic and diplomatic ally, opposes any military intervention and calls for a resolution through dialogue.
The third missile test in as many weeks is straining relations with the South and other neighbours. However, China is urging all sides to remain calm and exercise restraint.
The international body urged Kim Jong-un's regime to stop ballistic missile tests and threatened further sanctions if it failed to do so.
The missile was launched from an area called Panghyon in North Korea's western region and it flew about 500 km (300 miles), South Korean military says.
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