(CNN) North Korea, a tiny isolated state with a population the size of Texas, has left the world's most powerful nation with a diplomatic dilemma.

Senior figures in the Trump administration have ramped up their threats of military action in the wake of North Korea's successful test of an intercontinental ballistic missile (ICBM) but foreign policy experts say the only option going forward is a return to the negotiating table.

During a press conference in Poland Thursday morning, US President Donald Trump said he was considering "pretty severe things" in response to North Korea's "very, very bad behavior."

One day earlier, the US general leading troops in South Korea, Gen. Vincent K. Brooks, said only "self restraint" was preventing war, while US ambassador to the United Nations Nikki Haley said the US was prepared to use its "considerable military forces."

But for all the US' military posturing, experts say any form of military strike would be disastrous and out of the question.

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"Diplomacy is the best option," veteran diplomat and former New Mexico Governor Bill Richardson told CNN.

"It's not a good option because we don't know what Kim Jong Un wants ... but (to) just let the situation continue without any kind of diplomacy, without any kind of effort at mediation, I think is the wrong way to go."

Former British Charge D'Affaires to North Korea Jim Hoare told CNN there was a lot of "machismo" currently in the air between Washington and Pyongyang, with neither side wanting to back down.

"The basic problem is the US sees itself ... as a super power and here's this punk regime standing up to it, saying 'You can't tell us what to do'," he said.

North Korea's state media said its ICBM had reached an altitude of 2,802 kilometers (1,741 miles), the highest ever for a North Korean weapon.

The rogue state claimed it is now able to hit the American mainland with a nuclear warhead.

It has long been North Korea's goal to be taken seriously as a nuclear power and treated by the US as a peer.

"They want to be the big boys in the region. They want the US to talk to them directly without China ... I think we have to be careful in (our) response, not be provoked, not talk about preemptive strikes," said Richardson, who has traveled to North Korea several times on diplomatic missions.

What could negotiations look like?

Unofficial talks between North Korea and the United States do happen occasionally, as confirmed to CNN by Joe Cirincione, president of anti-nuclear advocacy group Ploughshares Fund , Wednesday.

But no official negotiations between the two countries have been held since a moratorium on weapons testing in exchange for food aid was agreed to in 2012.

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In attendance were representatives from the US, North Korea, China, Japan, Russia and South Korea, with the goal of dismantling the rogue state's nuclear program.

But then-North Korean leader Kim Jong Il regularly ignored resolutions made at the meetings and continued testing missiles or nuclear weapons, leading to the eventual breakdown in negotiations.

Adam Mount, senior fellow at the Center for American Progress, told CNN there might be reluctance in the Trump administration to enter into talks which could be messy and "unsatisfying."

"There's no easy win on the North Korean issue," he said. "Any agreement would be unsatisfying, prone to failure, so that has to make us really skeptical as to if a deal could be reached and if it could hold."

Why no military option?

US and South Korean troops held a ballistic missile drill Wednesday morning, the day after the North Korean launch, to demonstrate their ability to "(target) the enemy's leadership in case of emergency," South Korea's Defense Ministry said.

Several US officials have openly discussed their willingness to conduct a military strike on North Korea, including UN Ambassador Haley who said the US was prepared to use the "full range of our capabilities."

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"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.

US Gen. Brooks said American forces in South Korea were ready to make "resolute decisions any time." "Whoever thinks differently is making a serious misjudgment," he said.

But despite the strong words, diplomats and analysts said a military response was out of question in the face of a potentially-devastating North Korean reaction or even a regional war.

"Even a limited military strike could escalate to a major war. This is not Syria. You hit North Korea, they hit back," Cirincione said.

Writing for CNN, former British ambassador to North Korea John Everard said any war with North Korea would be "unspeakably horrible."

"It might be possible quickly to seize North Korea's major cities, the country's military might well fight to the bitter end," he said.

"North Korea would be likely to use its stocks of the nerve gas... and, of course, it has nuclear weapons."

Trump: 'So much for China'

Another option posed by foreign policy experts and US officials is for stricter sanctions on North Korea to force it to abandon its aggressive actions.

But on Wednesday both the US and China were each putting the onus on the other to rein in North Korea's weapon program, with Washington calling for sanctions while Beijing wants concessions from the Americans.

Chinese President Xi Jinping reiterated his call for the North Koreans to halt its weapons tests in exchange for the US and South Korea pausing large military drills.

The deal has long been China's preferred position to resolve tensions on the Korean peninsula, first suggested by Foreign Minister Wang Yi in March.

But US ambassador to the United Nations Nikki Haley placed the responsibility for stopping North Korea squarely on China's shoulders.

"Much of the burden of enforcing UN sanctions rest with China," she said, emphasizing 90% of North Korea's trade is still with China.

"We will work with China ... but we will not repeat the inadequate approaches of the past that have brought us to this dark day."

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US President Donald Trump also said China had failed to put pressure on North Korea, tweeting Wednesday that trade had grown 40% in the first quarter between the two nations. "So much for China working with us," he said.

But John Delury, associate professor at Yonsei University in Seoul, told CNN China had almost no influence left on North Korea and toughening sanctions would only work so far.

"China probably could add more pressure but the pressure's only useful if there's an escape route that we want the North Korean's to take," he said.

"The harder piece is the diplomacy and figuring out a negotiation ... the Chinese are maybe good for the sanction but ultimately the burden is on the US, North Korea and South Korea to do something."