Peres provided no proof to back up his claims, but his comments echoed similar allegations last month in which he accused Syria of providing Scud missiles to Hezbollah guerrillas in Lebanon.
Israel considers Iran its greatest threat because of suspicions that its nuclear program is ultimately aimed at producing weapons as well as its repeated threats to destroy Israel.
Peres said the reclusive North Korean regime has become a "duty free shop for long-range missiles and nuclear weapons." Israel was observing the smuggling trend with "open eyes," Peres said.
"These weapons flow straight to Iran, who arms and strengthens the world's global terror network, including Hezbollah in Lebanon and other groups in Syria," Peres said Sunday, before meeting with visiting Danish Foreign Minister Lene Espersen.
Israel, the United States and many European nations believe Iran is pursuing nuclear weapons under the cover of a civilian nuclear energy program. Iran's leaders deny that and say they are only after atomic energy and other peaceful uses of nuclear technology.
Espersen said the international community must present a united front against Tehran's nuclear work. She said Denmark is working with members of the European Union and the U.N. Security Council to impose tougher economic sanctions against Iran.
Israel has welcomed the international diplomacy, but refused to rule out military action if sanctions do not persuade Iran to fully cooperate with the efforts to ensure it doesn't direct its nuclear work toward weapons production.
Israeli defense officials have long believed North Korea is working with Iran to arm Israel's enemies. They say, for instance, that katyusha rockets fired into Israel by Lebanese Hezbollah guerrillas during a monthlong war in 2006 originated in North Korea.
In 2007, Israeli warplanes carried out an attack on Syria, targeting an installation that U.S. intelligence officials said was an unfinished nuclear reactor being built by North Korea.
Israeli military officials maintain that North Korea has supplied Iran with missiles as well as with the technological know-how to build their own weapons. Some of these weapons have reached Hezbollah, they say.
The U.S. and other nations accuse Iran of seeking to develop long-range intercontinental ballistic missiles and say North Korea has provided assistance or sold Tehran missile technology. Iran has always maintained its missile program is entirely domestic.
The most advanced missile known to be in Iran's arsenal is the medium-range Sajjil 2. It has a potential range of 1,200 miles — 2,000 kilometers — putting Israel, parts of southeastern Europe and U.S. bases in the Middle East within striking distance.
Peres stirred controversy recently by accusing Syria of smuggling Scud ballistic missiles to Lebanon, giving Hezbollah a new weapon that could strike deeper and harder at Israel than other weapons in its arsenal.
As a result of the allegations, the U.S. summoned the senior Syrian diplomat in Washington and charged Syria with "provocative behavior" that could spark a new conflict in the Middle East.
Syria denies any smuggling of weaponry to Hezbollah and its foreign minister compared the U.S. accusations to Washington's prewar claims against Iraq.
Peres repeated his warning Sunday.
"Syria must stop acting one way and speaking another way," he said. "Their support for terror can no longer be hidden."