(CNN) Americans have grown increasingly concerned that North Korea poses a very serious threat to the United States, according to a new CNN Poll conducted by SSRS .

Almost two-thirds of those polled, 62%, say Kim Jong Un's isolated dictatorship poses a deep threat to the US, up from 48% who said the same in March and the highest that figure has been in polling dating back to 2000.

That shift comes as 77% say they think North Korea is capable of launching a missile that would be able to hit the US.

The poll was completed after news reports of North Korean missile tests involving intercontinental ballistic missiles which have the potential to reach the US under the right conditions. Interviewing for the poll wrapped up on Monday, before an eventful Tuesday when news emerged that US intelligence believes North Korea has miniaturized a nuclear warhead and President Donald Trump threatened to respond to Pyongyang with "fire and fury" should they threaten the US.

The poll found that before those comments, Trump merited more negative than positive reviews for his handling of the situation with North Korea. Half (50%) say they disapprove of Donald Trump's handling of it, 37% say they approve and another 13% say they aren't sure about his handling of the issue.

With six in 10 people polled calling North Korea a very serious threat, the country is now viewed as a more serious threat than Iran (33%) or China (20%), and is about on par with the perceived threat posed by ISIS (64%). Fewer, however, said they saw the country's military and weapons capabilities as a crisis for the United States (32% saw it that way). That figure is higher now than it was in 2003, not long after the completion of the first round of six-party talks aimed at curtailing Pyongyang's efforts to obtain nuclear weapons. Back then, 22% considered the country's weapons and military capability to be a crisis.

Concerns about North Korea and views on its ability to hit the United States are similar across party lines, according to the poll. Among Republicans, 68% consider North Korea a very serious threat, that view is shared by a near identical 67% of Democrats. A matching 32% in each party call Pyongyang's military capabilities a crisis.

And about eight in 10 in each party say the country is capable of launching a missile that would hit the US.

Belief that North Korea is capable of launching a missile that could hit the United States has grown since 2009. Then, in a survey conducted not long after North Korea's underground detonation of what it said was a nuclear warhead, 72% said they thought the country was capable of hitting the United States with a missile.

Despite the 2009 polling, US intelligence assessments indicate that if North Korea does in fact have the capability of hitting the US with a missile under the right conditions, they obtained it recently.

On Tuesday, CNN reported that US intelligence analysts have assessed that North Korea has produced a miniaturized nuclear warhead, according to multiple sources, but it is not believed that the technology has been tested or that North Korea has the capability to deploy it with an intercontinental ballistic missile.

The public is split on whether the US should take military action in response to the country's recent weapons testing and development, and partisan divisions emerge on questions about how the US should respond. Overall, 50% say they favor taking military action in response to testing of weapons that could reach the US, 43% oppose it. Three-quarters of Republicans favor a military response (74%) but that dips to 47% among independents and 34% among Democrats.

Trump has frequently said that China should take a lead role in dealing with North Korea, and Americans generally agree, with 70% saying that China should take a major role in responding to the weapons testing. But just about as many, 68%, say that the US should take a major role.

This CNN Poll was conducted by SSRS by telephone August 3 through 6 among a random national sample of 1,018 adults. The margin of sampling error for results among the full sample is plus or minus 3.6 percentage points, it is larger for subgroups.