(CNN) North Korea should be kicked out of the United Nations, a Republican senator who is pressing other nations to support the idea told CNN on Tuesday.

Sen. Cory Gardner of Colorado, who chairs the Foreign Relations Subcommittee on East Asia, is asking 21 countries with embassies in Pyongyang to cut economic and diplomatic ties and support an expulsion of North Korea from the United Nations.

He says the "nefarious behavior" of North Korean leader Kim Jong Un, including nuclear tests and missile launches in defiance of UN resolutions, violated the UN's principles.

"Now is the time to diplomatically and economically isolate this regime, until it fully and irreversibly commits to peaceful denuclearization," he says in his letter.

In an interview with CNN, Gardner laid out his rationale. "We have to make it clear, if he wants to be part of a global environment of leadership, then he needs to back away, drop the nuclear program, and then he can be welcomed once again."

Four nations have expelled their ambassadors from North Korea since the country's latest nuclear test September 3: Spain, Mexico, Peru and Kuwait. In addition, Egypt and the Philippines dialed back their ties.

The Trump administration has been pushing countries to sever relations with the regime, including Vice President Mike Pence, who brought it up during his trip to Latin America last month.

Sen. Cory Gardner, a Colorado Republican

"The United States places great importance on the ongoing diplomatic isolation of the Kim regime," he said during a visit to Chile. "We strongly urged Chile today, and we urge Brazil Mexico and Peru, to break all diplomatic and commercial ties to North Korea."

The United States, like at least two dozen countries, already has no diplomatic relations with North Korea.

The United Nations has backed some of the Trump administration's efforts to sanction North Korea, including new sanctions banning coal exports and capping oil imports.

But one former Obama administration State Department adviser warns that expelling North Korea from the UN could have drawbacks.

"If you were to expel North Korea completely out of the international community, then what kind of channels of communication or leverage to you have?" said Vali Nasr, the dean of Johns Hopkins School of Advanced International Studies. "What sort of incentive would North Korea have in order to even engage in a conversation about denuclearization?"

He also raised other concerns: nations would not want to start a trend of blackballing each other; a potential backchannel for talks with North Korea would be lost; and Kim Jong Un's regime would react negatively.

"More than likely it will act even more erratically, because there are no relationships out there that he would preserve by acting better," he said. "And we will have even less knowledge of what's going on inside North Korea than we currently do."

But Gardner told CNN that a UN expulsion would incentivize the North Korean leader to reverse his weapons program.

"If Kim Jong Un wants to have legitimacy at the UN, if he wants to have legitimacy around the globe," said Gardner, "then he should know that we expect him to live up to the promises that he made over the last 20 years -- he and his father and grandfather made. And that is, denuclearization."

For a country to be expelled, a majority of the members of the UN general assembly would have to vote for it, according to a UN spokesman. A country has never been expelled, although Yugoslavia was suspended in the 1990s.

A spokesman for the American representative to the UN declined to comment. The National Security Council at the White House did not return CNN's calls or emails.

The North Korean delegation to the UN, which on Tuesday walked out of the chamber before President Donald Trump gave his speech, could not immediately be reached for comment. But North Korean state media has vowed that no sanctions will stop its nuclear and missile programs, and on Monday the country's Ministry of Foreign Affairs called the latest UN sanctions a "vicious, unethical and inhumane act of hostility to physically exterminate the people of" North Korea.

As to Gardner, North Korean state media has previously called him "human dirt ... who has lost basic judgment, and body hair," after the senator in May referred to Kim a "wack job."