"We have pretty much exhausted all the things that we can do at the Security Council at this point," Haley told CNN's State of the Union.
Haley added she was perfectly happy to hand the matter to Defence Secretary James Mattis.
"We're trying every other possibility that we have, but there's a whole lot of military options on the table," she said.
US National Security Adviser HR McMaster said North Korean leader Kim Jong-un is "going to have to give up his nuclear weapons because the president has said he's not going to tolerate this regime threatening the United States and our citizens with a nuclear weapon".
Asked if that meant Trump would launch a military attack against North Korea, McMaster said, "he's been very clear about that, that all options are on the table".
Kim has threatened Guam, a US territory in the Pacific, and has fired two missiles over Japan, a US ally in Asia, including one missile launched on Friday. North Korea also recently tested its most powerful nuclear bomb yet.
Secretary of State Rex Tillerson said he was waiting for the North to express interest in "constructive, productive talks".
"All they need to do to let us know they're ready to talk is to just stop these tests, stop these provocative actions, and let's lower the threat level and the rhetoric," he said.
Mattis said earlier this month, after Kim tested a hydrogen bomb, the US will answer any threat from the North with a "massive military response, a response both effective and overwhelming".
Trump has threatened to rain "fire and fury" on North Korea. Haley said that wasn't an empty threat from the president but, when asked, she declined to describe the president's intentions.
"If North Korea keeps on with this reckless behaviour, if the United States has to defend itself or defend its allies in any way, North Korea will be destroyed, and we all know that, and none of us want that," Haley said.
"None of us want war. But we also have to look at the fact that you are dealing with someone who is being reckless, irresponsible, and is continuing to give threats not only to the United States but to all their allies, so something is going to have to be done."
Source: News agencies