Pyongyang, a longstanding US adversary, has previously condemned the US-Israeli attack on Iran as an "illegal act of aggression".
Defying US President Donald Trump's desire to have a say in who runs Iran, the Islamic republic on Sunday named Mojtaba Khamenei to replace his father, longtime ruler Ali Khamenei, who died in an Israeli airstrike on February 28.
"We respect the rights and choice of the Iranian people to elect their supreme leader," Pyongyang's unnamed Foreign Ministry spokesperson was quoted as saying by the official Korean Central News Agency (KCNA).
The official said the United States and Israel are "destroying the regional peace and security foundations and escalating instability worldwide".
The spokesperson accused Washington and Israel of violating Iran's "political system and territorial integrity", and attempting to "overthrow its social system".
Such actions "deserve worldwide criticism and rejection as they can never be tolerated," the official added.
The United States has for decades led efforts to dismantle North Korea's nuclear programme, but summits, sanctions and diplomatic pressure have had little impact.
In recent months, the Trump administration has mounted a push to revive high-level talks with Pyongyang, eyeing a potential summit between the US president and the North's Kim Jong Un this year.
Trump said during his Asia trip in October that he was "100 percent" open to meeting with Kim, a remark that went unanswered by the North.
After largely ignoring those overtures for months, Kim recently said that the two nations could "get along" if Washington accepted Pyongyang's nuclear status.
Pyongyang's state media also said on Wednesday that North Korea's leader oversaw another test-firing of strategic cruise missiles from the naval Choe Hyon destroyer.
North Korea carried out a similar missile test from the vessel last week, claiming the country was in the process of "arming the Navy with nuclear weapons".
During the occasion, Kim stressed the importance of expanding a "powerful and reliable nuclear war deterrent," KCNA said.
Images released by state media showed Kim overseeing the launch remotely via video footage with his teenage daughter, Ju Ae, who is now widely regarded as his heir apparent.
There, Kim said "important successes" have been made in the practical deployment of "strategic and tactical strike means".
South Korea's spy agency has said Pyongyang appears to have begun the process of designating Ju Ae as leader Kim's successor, with the North frequently releasing photographs of the young daughter accompanying her father on official duties.
The test came as Washington and Seoul kicked off their springtime military drills "Freedom Shield" on Monday, to which Pyongyang responded by warning of "unimaginably terrible consequences".
The Choe Hyon is one of two 5,000-ton destroyers in the North's arsenal, both launched last year as Kim seeks to ramp up the navy with short-range tactical missiles capable of carrying nuclear warheads.
North Korea appears to be "securing the legitimacy and justification for bolstering war deterrence," Yang Moo-jin, former president of the University of North Korean Studies, told AFP.
With the war in Iran, the joint US-South Korea drills are being highlighted by the North "as not merely defensive and routine, but ultimately attempts at a preemptive war".
