U.S. Ambassador to the United Nations Nikki Haley said the U.S. is going to "push hard" against China amid threats from North Korea, and that China needs to do more when it comes to the country that just days ago test-launched an intercontinental ballistic missile (ICBM).

"We're going to go ahead and push for a strong resolution against North Korea," Haley told CBS News' John Dickerson on "Face the Nation." "I think it will be very telling based on how other countries respond whether they want to hold Kim Jong Un's hand through this process or whether they want to be on the side of so many countries who know that this is a dangerous person with the access to an ICBM."

"We're going to push hard not just on North Korea, we're going to push hard on other countries who are not abiding by the resolutions and not abiding by the sanctions against North Korea," she said. "And we're going to push hard against China because 90 percent of the trade that happens with North Korea is from China and so while they have been helpful, they need to do more."

Haley -- asked if China would ever lose its trade relationship with the United States if it fails to do more when it comes to North Korea -- did not rule out limiting trade, calling it "one of the ammunition options we have on the table."

"We do a lot of trade with a lot of countries," Haley said. "If there is a country that we don't think is looking out for our security and looking out for our confidence in that, then yes," Haley said.

"This is encouraging and motivating China to say, look, we appreciate what you've done. This is a whole new level. This is an ICBM test. We need you to not only do more but we need the pressure on North Korea and China has the ability to do it. They know that. We know that and we need to see some more action going accordingly. And I think the resolution is going to be a really big test on that," Haley added.

Haley described North Korea's test of an ICBM earlier this month -- on July Fourth -- as "hugely dangerous" not only for the United States, but also for allies around the world.

"You know, I mean how many tests does it take and how many more times do we have to tell them no escalation?" Haley said. "The fact that they launched an ICBM test is hugely dangerous not just for us but for so many of our friends in the world and we've got to put a stop to it."

President Trump returned to the U.S. Saturday night from the G-20 summit in Hamburg, Germany, where he met with multiple world leaders about how to handle North Korea and its leader, Kim Jong Un. At the summit, Mr. Trump dubbed North Korea a "problem and a menace."