The National Security Council has presented President Donald Trump with options to respond to North Korea's nuclear program — including putting American nukes in South Korea or killing dictator Kim Jong-un, multiple top-ranking intelligence and military officials told NBC News.

Both scenarios are part of an accelerated review of North Korea policy prepared in advance of Trump's meeting with Chinese President Xi Jinping this week.

The White House hopes the Chinese will do more to influence Pyongyang through diplomacy and enhanced sanctions. But if that fails, and North Korea continues its development of nuclear weapons, there are other options on the table that would significantly alter U.S. policy.

The first and most controversial course of action under consideration is placing U.S. nuclear weapons in South Korea. The U.S. withdrew all nuclear weapons from South Korea 25 years ago. Bringing back bombs — likely to Osan Air Base, less than 50 miles south of the capital of Seoul — would mark the first overseas nuclear deployment since the end of the Cold War, an unquestionably provocative move.

"We have 20 years of diplomacy and sanctions under our belt that has failed to stop the North Korean program," one senior intelligence official involved in the review told NBC News. "I’m not advocating pre-emptive war, nor do I think that the deployment of nuclear weapons buys more for us than it costs," but he stressed that the U.S. was dealing with a "war today" situation. He doubted that Chinese and American interests coincided closely enough to find a diplomatic solution.

An undated file photograph released by the North Korean Central News Agency (KCNA) shows North Korean leader Kim Jong-un overseeing Korean People's Army military exercise in Pyongyang, North Korea. KCNA/EPA/REX/Shutterstock / Shutterstock

"I don’t think that [deploying nuclear weapons] is a good idea. I think that it will only inflame the view from Pyongyang," retired Adm. James Stavridis told NBC News. "I don't see any upside to it because the idea that we would use a nuclear weapon even against North Korea is highly unlikely."

Two military sources told NBC News that Air Force leadership doesn't necessarily support putting nuclear weapons in South Korea. As an alternative, it's been practicing long-range strikes with strategic bombers — sending them to the region for exercises and deploying them in Guam and on the peninsula as a show of force.

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Mark Lippert, the former U.S, ambassador to South Korea, said nuclear deployment there is a concept that's been embraced by a growing number of Koreans.

"Some polls put it at well over 50 percent," he said. "It's something that's being debated, and support for it over time, at least at this point, is climbing."

Still, he thinks it's a bad idea, undermining the U.S. objective of a nuclear-free zone and "South Korea's moral authority toward de-nuclearization of the peninsula."

A woman walks past a television screen showing file footage of a North Korean missile launch, at a railway station in Seoul on April 5, 2017. Jung Yeon-Je / AFP - Getty Images

Another option is to target and kill North Korean leader Kim Jong-un and other senior leaders in charge of the country's missiles and nuclear weapons and decision-making. Adopting such an objective has huge downsides, said Lippert, who also served as an assistant defense secretary under President Barack Obama.

"Discussions of regime change and decapitation...tend to cause the Chinese great pause of concern and tends to have them move in the opposite direction we would like them to move in terms of pressure," he said.

Stavridis, a former NATO commander, said that "decapitation is always a tempting strategy when you're faced with a highly unpredictable and highly dangerous leader."

"The question you have to ask yourself," he said, "is what happens the day after you decapitate? I think that in North Korea, it's an enormous unknown."

A third option is covert action, infiltrating U.S. and South Korean special forces into North Korea to sabotage or take out key infrastructure — for instance, blowing up bridges to block the movement of mobile missiles. The CIA, which would oversee such operations, told NBC News it could offer "no guidance" on this option. But Stavridis said that he felt it was the "best strategy" should the U.S. be forced to take military action. He described such action as: "some combination of special forces with South Korea and cyber."

Last year, South Korea announced the creation of a special operations unit called Spartan 3000 to operate behind enemy frontlines inside North Korea.

Trump has already indicated he's open to unilateral action if China fails to rein in its ally, telling the Financial Times over the weekend, "If China is not going to solve North Korea, we will."

But on Wednesday, Gen. John Hyten, commander of U.S. Strategic Command, told the Senate Armed Services Committee that "any solution to the North Korea problem has to involve China." He said that while his job was to present "military options" to the White House, he finds it "hard ... to see a solution without China."

Related: Defense Secretary Says North Korea 'Has Got to be Stopped'

Still, military exercises and simulations focused on North Korea have been getting larger and more complex in recent years. In 2017 alone, these exercises have included;

"Key Resolve," a command post exercise held in March

"Foal Eagle," a peninsula-wide mobilization and logistics exercise underway now,

An anti-submarine exercise taking place this month, part of the "Silent Shark" series.

"Nimble Titan," a gigantic multinational missile defense synchronization experiment last month.

And last month, the Army announced that it would permanently station its version of the armed Predator — called Gray Eagle — on the Korean Peninsula. That follows an exercise last summer in which hunter-killer Reaper drones practiced the mock destruction of North Korean mobile missile launchers.

Since North Korea’s first successful nuclear test in 2009, the United States has adopted a strategy to "slow, stop, and defeat" the North’s nuclear and ballistic missile pursuits. That ranges from interdiction of supplies to interception of a ballistic missile actually in the air.

The Trump White House, through the National Security Council, asked for blue sky options in early February, a senior official told NBC on background. "Think big," the official said that the agencies were instructed. Many proposals have already been abandoned, but on the military side, sources say, the three options with the highest impact still constitute the next steps.

"It is absolutely appropriate," Stavridis said, for all contingencies to be considered. "In fact, it's mandatory for the Pentagon to present the widest possible array of options. That's what enables presidents to make the right decisions, when they see all the options on the table in front of them."