After a top Pentagon official said the only way to destroy North Korea’s nuclear weapons program would be through a ground invasion, a senior Senate Democrat urged the secretary of state, Rex Tillerson, to “stay the course” and achieve a diplomatic solution to the crisis, in spite of Donald Trump’s unpredictable behaviour and threats of military action.

“The worst alternative is a war which could become nuclear,” Dianne Feinstein said on Sunday.

Trump himself threw a characteristic wildcard into the mix, saying he would “certainly be open” to meeting the North Korean leader, Kim Jong-un.

Rear Adm Michael J Dumont of the joint staff offered his blunt assessment of US options in response to a letter from two congressional Democrats who asked about casualty assessments in any conflict with North Korea.

The US is evaluating Pyongyang’s ability to target heavily populated areas of South Korea with artillery, rockets and ballistic missiles, Dumont said, adding that Seoul, the South’s capital with a population of 25 million, is just 35 miles from the demilitarized zone (DMZ).

Casualties would differ depending on advance warning and the ability of US and South Korea forces to counter such attacks, Dumont said, also mentioning the possibility that chemical and biological weapons might be used by the North.

“It is the most bleak assessment,” Feinstein, a member of the Senate intelligence committee, told CNN’s State of the Union. “I’ve spent a lot of time reading the intelligence. I’ve had an opportunity to discuss the situation with [Defense] Secretary [James] Mattis. I believe that an outbreak of war would kill hundreds of thousands of people.”

Dumont’s views were made public as Trump began a visit to Asia in which North Korea and Kim Jong-un’s nuclear ambition loom large. “No one, no dictator, no regime … should underestimate American resolve,” he told a military audience at Yokota airbase near Tokyo on Sunday on the first leg of his five-country trip that will also take in South Korea, China, Vietnam and the Philippines.

The president has repeatedly threatened North Korea, saying in his maiden speech at the United Nations in September he would “totally destroy” the country if necessary. He has also repeatedly undercut Tillerson in his efforts to pursue talks with the regime in Pyongyang.

Trump has also said before that he would be willing to meet Kim. In an interview with the Sinclair TV show Full Measure broadcast on Sunday morning, he said he was holding meetings with numerous Asian leaders and “would sit down with anybody.

“I don’t think it’s strength or weakness, I think sitting down with people is not a bad thing. So I would certainly be open to doing that but we’ll see where it goes, I think we’re far too early.”

Feinstein said she was “very pleased that Secretary Tillerson is with the president [in Asia]. I think if he will stay the course and use diplomacy the way diplomacy can be used, that it might be possible to work something out.”

Also speaking to CNN on Sunday another senior Democrat, House minority leader Nancy Pelosi, said the US should “exhaust every possible diplomatic resolution”. She also said Trump’s approach to North Korea was akin to “poking a stick in the eye of a mad dog”.

Donald Trump warns 'dictators' not to underestimate American resolve – video

Feinstein said she was concerned about Trump’s behaviour on a high-stakes trip during which, the president told reporters on Air Force One, he expects to meet the Russian president, Vladimir Putin. Both men are due to attend the Asia-Pacific Economic Cooperation (Apec) summit in Da Nang, Vietnam.

“Everybody sees what the flaws in this president are,” Feinstein said. “There’s no question about it … Can he actually stay on script?

“I watched his remarks in Japan with respect to the military that was receiving him and I thought he did a good job. He stayed on script. It’s when he goes off script, it’s when he tweets, it’s where he has to attack everybody if he feels even slightly aggrieved.”

Feinstein also referred to Trump’s comment in a Fox News interview this week that vacancies at the state department were not a concern because he was “the only one that matters”.

“He isn’t the only one that matters,” she said. “He’s the one that’s there to solve problems on behalf of the United States and that’s what this trip is about and I hope and trust that he sticks to that mission.”

Representatives Ted Lieu of California and Ruben Gallego of Arizona wrote the original letter to Dumont. He answered: “A classified briefing would be the best place to discuss in detail the capability of the US and its allies to … counter North Korea’s ability to respond with a nuclear weapon and eliminate North Korea’s nuclear weapons located in deeply buried, underground facilities.”

On Saturday, 15 Democrats and one Republican member of Congress, all military veterans, called Dumont’s assessment “deeply disturbing” and said such an action “could result in hundreds of thousands, or even millions of deaths in just the first few days of fighting”.

In a joint statement, the lawmakers said: “It is our intent to have a full public accounting of the potential cost of war, so the American people understand the commitment we would be making as a nation if we were to pursue military action.”

They also said the Trump administration “has failed to articulate any plans to prevent the military conflict from expanding beyond the Korean peninsula and to manage what happens after the conflict is over”.