"We've got to improve the Iran agreement to the point where it's also something that could serve as a model for North Korea. But persuading countries not to go nuclear is hard," said Negroponte, who served in several roles in the George W. Bush administration. In addition to U.N. ambassador, Negroponte was deputy secretary of State and director of National Intelligence under the Republican 43rd president.
"We have to think about triangulating between Iran and North Korea," Negroponte added in a "Squawk Box" interview.
Iran announced last month it was scaling back on its compliance with major world powers its nuclear agreement, one year after Washington announced it was pulling out of the deal. Last week, President Donald Trump imposed new sanctions on Iran after it allegedly shot down an American military drone and attacked oil tankers in the vital Strait of Hormuz shipping route.
On Monday, Iran's foreign minister said the country had breached the limit of its enriched uranium stockpile, which was set in the 2015 multination nuclear deal. On Friday, European officials attempted to persuade Iran to stop development by offering trade incentives, but the assistance was not enough.
Looking to halt Pyongyang's nuclear ambitions, Trump had met back in February with North Korean leader Kim Jong Un. However, that summit was cut short after Trump announced a deal could not be reached. The White House was pushing for North Korea to give up its nuclear weapons for an economic boost.
On Sunday, Trump met Kim and became the first sitting U.S. president to visit the North Korean side of the Demilitarized Zone. The two leaders said they would resume negotiations.
The impromptu Trump-Kim meeting may have set up the path for a deal, Negroponte said. "Not much else has worked in the past," he added, while advocating giving Trump's approach a chance. "Over the past 25 years, we've gone one step forward two steps back."