Washington(CNN) The Trump administration is considering military action against North Korea if the rogue regime successfully builds a nuclear missile capable of hitting the United States, according to multiple sources with knowledge of the administration's latest thinking. Senior national security officials believe a nuclear armed Pyongyang represents an unacceptable risk to the US.

Beyond the missile threat to the US homeland, the national security officials pushing for military action believe that if North Korea becomes a full nuclear power, it will proliferate, potentially sharing nuclear and missile technology with states such as Iran, Pakistan and Libya, and non-state actors.

Such a prospect would increase the nuclear threat to US interests. That possibility, according to these officials, is ultimately more dangerous to the US and the region than conventional military action to thwart Pyongyang's nuclear ambitions, despite the risk of significant civilian and military casualties in such a conflict.

"All the damage that would come from a war would be worth it in terms of long-term stability and national security," Senator Lindsey Graham, a South Carolina Republican who has had multiple conversations with President Donald Trump about North Korea, told CNN.

On Thursday Trump spoke with President Moon Jae-in of South Korea, and the White House readout of the call stated that the two leaders "noted their firm position that any dialogue with North Korea must be conducted with the explicit and unwavering goal of complete, verifiable, and irreversible denuclearization."

Another hostile step by the North, such as conducting another intercontinental ballistic missile test, would increase the chances of a US military response.

Beyond the proliferation risk, those arguing for military action believe a nuclear North Korea would be emboldened to use conventional military forces and other pressure against US allies South Korea, Japan and others in the region to accomplish strategic goals including steps toward the eventual reunification of the Korean Peninsula on North Korean terms. This assessment of North Korea's intentions, while not perfect, is based in part on improved US intelligence on North Korea over the course of the last year.

The US also fears that if North Korea becomes a full nuclear power Japan may follow suit, sparking a destabilizing nuclear arms race in the region.

"I'm completely convinced that President Trump and his team reject the policy of containment," Graham told CNN. "They've drawn a red line here and it is to never let North Korea build a nuclear tipped missile to hit America."

Multiple officials cautioned that a diplomatic solution currently remains the administration's focus -- and that there are ways to block North Korea's missile development short of all-out war, including covert means.

In addition, the US and its allies continue to pursue a policy of exerting maximum economic and political pressure on Pyongyang aimed at preventing the regime from perfecting its long-range nuclear missile capabilities and bringing the rogue regime to the negotiating table.

The presence of a North Korean delegation at the Olympic Games in South Korea prompted US hopes of diplomatic progress, and the administration considers North Korea's recent offer of direct talks a potentially positive sign.

At a public forum last month, CIA Director Mike Pompeo said, "The President is intent on delivering a solution through diplomatic means," adding that, "we are equally, at the same time, ensuring that if we conclude that is not possible that we present the President with a range of options that can achieve his stated intention."

US military options against North Korea include steps short of military action, such as imposing a naval blockade on the north, officials have said.

North Korea, however, said in a statement Sunday that it considers "any type of blockade an act of war against us."

Key voices within the administration, including Trump's national security adviser H.R. McMaster have insisted that a military strike be considered as a serious option to exact maximum pressure on Pyongyang, sources have previously told CNN.

Another faction -- led by Defense Secretary James Mattis and Secretary of State Rex Tillerson -- has long opposed the idea of using military force before all other options have been exhausted.

The recent loss of key diplomatic voices -- such State Department official Joseph Yun and the onetime pick for US ambassador to South Korea, Victor Cha -- could also precipitate a more hawkish consensus within the White House, according to CNN military analyst John Kirby.

North Korea has a long history of weapons proliferation, supplying missiles and missile technology to countries in the Middle East and South Asia -- including Egypt, Iran, Libya, Pakistan, Syria and Yemen -- in exchange for hard currency.

Pyongyang has also been known to export dual use materials relevant to nuclear activities. The United Nations reports annually on adherence to sanctions and has flagged that North Korea helped Syria to build an undeclared nuclear reactor. And in November 2012, the UN said North Korea allegedly attempted to sell graphite rods to Syria.

Several US officials have downplayed previous suggestions that the administration is considering the use of a so-called "bloody-nose strike" -- a military option that would be significant enough to force North Korea to question its nuclear ambitions but limited in scale as to avoid retaliation.

Republican Sen. James Risch of Idaho said earlier this month that lawmakers have been told "by administration people, about as high up as it gets, that there is no such thing as a 'bloody nose strategy' " and that the option has never been discussed.

Pyongyang tested a new missile on November 28 that flew higher and farther than any previous launch and bragged afterward that its new Hwasong-15 could deliver nuclear warheads anywhere in the US.

But Mattis said in December that he does not believe that North Korea's current intercontinental ballistic missiles are capable of hitting the continental US.

North Korea's November ICBM "has not yet shown to be a capable threat against us right now," Mattis said at the time.