The US has said it will use its "considerable military forces" on North Korea "if we must", following Tuesday's long-range missile test.
US ambassador to the UN Nikki Haley said a new resolution will also be tabled against Pyongyang at the United Nations.
She described the test as a sharp military escalation and also threatened to use trade restrictions.
Hours after she spoke, the US and South Korea fired more missiles into the Sea of Japan as part of military drills.
But Pyongyang has said it would not negotiate unless the US ends its "hostile policy" against North Korea.
Tuesday's missile launch, the latest in a series of tests, was in defiance of a ban by the UN Security Council.
Meanwhile, US Defence Secretary Jim Mattis and his Japanese counterpart Tomomi Inada said the test was an "unacceptable provocation".
A statement released by the US defence department said the two spoke on the phone, where Gen Mattis said the US was committed to defend Japan and provide deterrence.
On Wednesday Ms Haley warned that North Korea's test launch of an intercontinental ballistic missile (ICBM) was "quickly closing off the possibility of a diplomatic solution".
"The United States is prepared to use the full range of our capabilities to defend ourselves, and our allies," she told the UN Security Council, which met for an emergency session to discuss the test.
"One of our capabilities lies with our considerable military forces. We will use them, if we must, but we prefer not to have to go in that direction," she said.
On Thursday in South Korea, the US held a joint military drill with the South's troops for a second day in response to the long-range missile test.
It involved various destroyers, warships and fighter jets launching guided missiles against a simulated maritime attack, reported Yonhap news agency.
Ms Haley also said the US could cut off trade with countries which continued to trade with North Korea in violation of UN resolutions.
"We will look at any country that chooses to do business with this outlaw regime," she said.
Earlier, US President Donald Trump criticised China for its trade with North Korea.
Mr Trump has arrived in Warsaw where he is due to meet Chinese President Xi Jinping for the second time. He will later travel to Hamburg for the G20 summit, where world leaders are expected to discuss the missile test.