Secretary of State Colin Powell said Tripoli's decision had put the United States and its allies "on a bit of a roll," and states still pursuing chemical, biological and nuclear weapons would be better off if they followed suit.
"We hope that the North Koreans are watching all of this, and realizing that others are getting smart, and it's time for them to get smart too," Powell said in an interview with syndicated radio talk show host Michael Reagan, son of former US president Ronald Reagan.
The same thing applied to Iran, the secretary of state pointed out, adding that Syria needed "to get out of the hole that you have been in for all these years."
Libyan leader Colonel Moamer Kadhafi issued a similar appeal to the three nations on Monday.
Powell, who is currently recovering at home after prostate cancer surgery, attributed success with Libya to the right mix of diplomatic and military pressure employed by the administration of US President George W. Bush and vowed to continue using both of these tools.
"So, diplomacy, force and diplomacy -- they have to be married up and each used in the service of the other," he said.
Kadhafi stunned the world last Friday, when he announced that his country had renounced its quest for all chemical, biological and nuclear weapons and would allow thorough international inspection to prove its good will.
The announcement, confirmed by British Prime Minister Tony Blair and Bush, capped nine months of secret diplomacy by the United States and Britain aimed at bringing about Libya's turnaround.
Powell said Syria has been doing a better job working with US troops along the border with Iraq but needed to change its behavior in other areas.
"Syria still doesn't get it that they have to abandon support of terrorist activity," said the secretary of state. "They've got to return any Iraqi monies that they might have in their bank, and they've started to take some minor actions in that regard."
He did not elaborate, but the dispute reportedly involves about 250 million dollars in Iraqi funds deposited in the state-owned Commercial Bank of Syria.
Syria acknowledges the funds exist, but argues they must first be used to pay private Syrian companies to which the deposed Iraqi government of Saddam Hussein owed money, The Wall Street Journal reported earlier this month.
Powell said he believed Iran "has now been more forthcoming" toward the international community "and starting to acknowledge that it had programs that it had denied it possessed earlier."
Iran signed a protocol to the nuclear Non-Proliferation Treaty last week, which allows surprise inspections of its nuclear sites by the International Atomic Energy Agency.
The secretary of state called the stalled Middle East peace process "the most vexing challenge" he is facing on his job, but said that while the United States has not made progress on the roadmap to peace, there was, as he put it, "a lot of churning going on now."
He said he hoped Israeli Prime Minister, Ariel Sharon, and his Palestinian counterpart, Ahmed Qorei, would meet in coming weeks and promised a vigorous push next year toward a negotiated settlement in the region.
"We'll be making this a major priority along with the global war on terror, and along with making sure that we consolidate our victories in Iraq and Afghanistan, and then with all the other many items that are on the president's foreign policy agenda," Powell stated.