The US has said that it will use its "considerable military forces" on North Korea "if we must".
Describing the North's latest missile test as a sharp military escalation, US Ambassador to the United Nations Nikki Haley said the US would table a new resolution against Pyongyang.
Ms Haley also threatened to use trade restrictions.
The missile launch, the latest in a series of tests, was in defiance of a ban by the UN Security Council.
North Korea's test launch of an intercontinental ballistic missile (ICBM) on Tuesday was "quickly closing off the possibility of a diplomatic solution," Ms Haley said.
"The United States is prepared to use the full range of our capabilities to defend ourselves, and our allies," the US ambassador told the UN Security Council, meeting 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."
The French ambassador told the council that France also favours a new resolution on North Korea, which would tighten sanctions.
Russia, which condemned the test, said the possibility of using military measures "should be excluded".
China's representative said Beijing found North Korea's actions unacceptable. But he repeated China and Russia's joint call for the US to reverse plans to deploy an anti-missile system in South Korea, and for the two countries to suspend their joint military exercises close to North Korea.
Both Russia and China are permanent members of the UN Security Council and could veto any new resolution.
Earlier, Donald Trump criticised China for its trade with North Korea.
Ms Haley, who said she had discussed the issue with the president, said the US could cut off trade with countries which continued to trade with North Korea in violation of US resolutions.
"We will look at any country that chooses to do business with this outlaw regime," she says.
Mr Trump has arrived in Warsaw, ahead of his trip to Hamburg for the G20 summit of major economies, where he is due to meet Chinese President Xi Jinping for the second time.
The US president held talks with China's leader Xi Jinping at his Mar-a-Lago retreat in Florida in April.
After those talks, Mr Trump hailed "tremendous progress" with China, but on Wednesday the US president tweeted: "So much for China working with us - but we had to give it a try!"
North Korea's test of a long-range missile, which some experts think could travel far enough to hit Alaska, will be the subject of talks between leaders at the G20, which includes Russia.
Tuesday's launch was North Korea's first-ever test launch of an intercontinental ballistic missile (ICBM).
State news agency KCNA quoted leader Kim Jong-un as saying the test was a "gift" to the Americans on their independence day.
The report warned of the possibility of more tests, saying he had ordered officials to "frequently send big and small 'gift packages' to the Yankees".
Pyongyang said earlier the Hwasong-14 ICBM had reached an altitude of 2802km and flew 933km for 39 minutes before hitting a target in the sea.
North Korea, it said, was now "a full-fledged nuclear power that has been possessed of the most powerful inter-continental ballistic rocket capable of hitting any part of the world".