Washington(CNN) Two in three Americans say President Donald Trump should not pull the United States out of the nuclear deal aiming to block Iran from developing nuclear weapons, according to a new CNN poll conducted by SSRS.

Trump announced his intent to decertify the agreement last week. But eight in 10 Democrats and two in three independents oppose withdrawing from the agreement. Even in the President's own party, Republicans are evenly split, with 48% wanting to remain and 47% to withdraw.

Concern about Iran has slipped among Americans since the deal was put in place. Only three in 10 adults say the threat is "very serious," down from nearly half, 49%, in September 2015. That marks the smallest share of those concerned in CNN polling dating back to 2000. Still, nearly seven in 10 adults overall, 69%, say Iran poses a serious threat to the US.

Republicans are more likely to view Iran as a very serious threat than Democrats, 45% versus 26%. But only half the gap that existed two years ago, when Republicans were 36 points more likely than Democrats to see Iran as a deeply serious threat.

After Trump announced his decision on the deal, Iran's supreme leader, Ayatollah Ali Khamenei, said in public comments on Wednesday that "it would be a waste of time to respond to such blatherings and nonsensical remarks by the foul-mouthed US President."

The North Korean threat

Americans view North Korea as a far greater threat -- and have growing concerns about how Trump is handling the escalating situation. An overwhelming 86% of Americans say that North Korea poses a serious threat to the US. More than six in 10 (62%) label the rogue nation a "very serious" threat, the same as in August, matching the highest level in CNN polls dating back to 2000.

When considering Trump's responses to North Korea's threats, more than six in 10, 63%, say they have been more reckless than responsible. These views are divided starkly by party: 88% of Democrats say Trump has been more reckless, though a sizable 27% of Republicans agree. About two-thirds of independents (65%) say he's been reckless.

North Korea and the United States have been in an escalating war of words over the last several months. Trump has promised "fire and fury like the world has never seen," but North Korea continues to test nuclear weapons and long-range missiles.

Disapproval of Trump's overall handling of the situation with North Korea is also on the rise. A majority, 57%, disapprove of the way the President is handling North Korea, up from a 50% disapproval in September. His approval on handling the situation stands at 37%.

Americans of both parties are equally likely to view North Korea as a serious threat: 89% of Democrats and 90% of Republicans do, while 83% of independents say the same.

Other threats around the globe

Despite the high anxiety around North Korea, a smaller share of Americans, 48%, say they are worried that they or their families will become victims of a nuclear attack on the US. A narrow majority are not that worried (51%). Deep worries are higher outside the Midwest, but there are not large differences across regions of country.

Also, concern increases with age: Only 16% of Americans under 35 years old say Iran poses a "very serious" threat versus 41% of people over 65 years old. And less than half, 49%, of people under 35 view North Korea as a "very serious" threat versus 70% of those over 45.

The poll also found that 69% of Americans say that Russia poses a serious threat to the United States. Democrats are more than twice as likely as Republicans to call the country that US intelligence says meddled in the 2016 election a "very serious" threat, by a 45% to 19% margin.

Still, majorities of both parties call the nation a threat overall. Just 24% say that Cuba poses a serious threat to the United States, the lowest in CNN polling back to 1983.

The CNN poll was conducted by SSRS by telephone from September 17 to 20 among a random national sample of 1,053 adults. The margin of sampling error for results among the full sample is plus or minus 3.7 percentage points; it is larger for subgroups.