Mr Trump could launch a pre-emptive strike on North Korea to destroy its nuclear and missiles programmes, but that would be at the cost of North Korea's retaliation aimed at Seoul, which is located just 60 kilometres from the demilitarised zone and home to 10 million people.
In all, six sets of sanctions have been imposed on North Korea since it first tested an atomic device in 2006.
Ambassador Nikki Haley said the U.S.is prepared to defend itself and its allies.
But he also said it was "hard to believe" that South Korea and Japan, the two USA treaty allies most at risk from North Korea, would "put up with this much longer". "There is no formula, no path forward, other than war, that isn't built on some degree of common cause between Washington and Beijing".
The country also vowed to keep sending to the United States government more "gift packages" of weapons tests.
"The North Korean regime is causing tremendous problems and is something that has to be dealt with, and probably dealt with rapidly". And it says all options are on the table.
In addition, the USA did not insist on mentioning the Terminal High Altitude Area Defense system in the joint statement.
The test, North Korea's most successful yet, is a direct rebuke to President Donald Trump's earlier declaration that such a test "won't happen!"
Meeting with his German counterpart in Berlin, the South Korean president said it was imperative to increase global pressure on North Korea, but that they must still seek to engage with the reclusive state.
KCNA said it had a carbon composite nose cone that could carry a "large, heavy nuclear warhead" and survive the harsh conditions of re-entry into the Earth's atmosphere - including "heat reaching thousands of degrees centigrade" - to "accurately hit the target".
And China might not be the only nation inconvenienced if there were a serious effort to choke off the North's supply of hard currency; North Korean workers have been contracted out in Russia, Qatar and, until a year ago, even democratic Poland.
North Korea's leader is considered unstable and his regime is a brutal one.
The regime's Korean Central News Agency said Kim expected the USA would be "displeased" by Pyongyang's achievement, and urged his scientists to conduct further tests as "big and small "gift packages" to the Yankees".
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Previously, North Korea had demonstrated missiles of short and medium range.
Hailey said the US' focus was on how to push through tighter sanctions.
So President Trump told reporters in the Rose Garden last week. Does this guy have anything better to do with his life? South Korea and Japan therefore have to make it clear to the U.S. leader that this strategy is too risky.
"Much of the burden of enforcing United Nations sanctions rests with China", she said.
"This guy" presumably refers to Kim.
Its enforcement would rest with Beijing, she said, because 90 percent of trade with North Korea was with China.
Tuesday's ICBM launch, confirmed by United States and South Korean officials, was a milestone in North Korea's efforts to develop long-range nuclear-armed missiles.
220893220880220880U.S. calls for global diplomatic effort to sway North KoreaNorth Korea's Tuesday missile launch crossed the intercontinental threshold the US had been hoping to prevent.
During his trip, Trump will meet for the second time with Chinese President Xi Jinping, with whom he has expressed frustration for failing to use enough leverage to curb North Korea's nuclear program.
But even if that 30% drop is real, China still trades with North Korea far more than it did as recently as 2010.
The missile flew higher and longer than previous ones North Korea has launched, sparking concerns around the world.
While the envoys of the United Kingdom and France echoed Haley's sentiments, the ambassador of Sweden said that the crisis on the Korean peninsula does not have a military solution, and warned that the potential for mistakes and misunderstandings was high.
Experts caution that US missile defenses are now geared to shooting down one, or perhaps a small number of basic, incoming missiles.