The double attack killed at least 23 people and wounded almost 150 and heightened fears that Lebanon will be sucked into Syria's civil war.
The 15-member Security Council and Ban released statements that "strongly condemned" the attack.
The council "appealed to all Lebanese people to preserve national unity in the face of attempts to undermine the country's stability."
It "stressed the importance for all Lebanese parties to respect Lebanon's policy of disassociation and to refrain from any involvement in the Syrian crisis."
The UN secretary general "calls on all in Lebanon to recognize that such appalling and indiscriminate acts of violence target all in Lebanon," said deputy UN spokesman Farhan Haq.
"He urges all Lebanese parties to act with restraint and to support the institutions of the state, and particularly the security forces, as they seek to prevent further acts of terrorism."
UN political chief Jeffrey Feltman on Tuesday highlighted to the UN Security Council reports that Lebanese militia Hezbollah was fighting with President Bashar al-Assad's forces in Syria "in clear violation" of a statement by Lebanese parties to stay out of the war.
US condemns 'senseless and despicable' Lebanon bombings
US Secretary of State John Kerry Tuesday condemned what he called the "senseless and despicable" bomb attacks against Iran's embassy in Beirut, calling on all parties to back Lebanon's probe.
"The United States knows too well the cost of terrorism directed at our own diplomats around the world, and our hearts go out to the Iranian people after this violent and unjustifiable attack," Kerry said in a statement.
Russia condemns 'terrorist act' in Beirut
Russia on Tuesday strongly condemned as a "terrorist act" the double suicide bombing outside the Iranian embassy in Beirut that killed at least 23 people.
Moscow deplored the "bloody attack" targeting a "diplomatic mission" and called for punishing those responsible for fomenting violence in the volatile region, the Russian foreign ministry said in a statement.
"The incident again underscores the need to stop those who via a series of bloody attacks in Lebanon, in Syria, in Iraq and other countries in the Middle East and north Africa, seek to rekindle hatred between faiths, which is disastrous for the region and its people," the statement said.
The attack, which also wounded almost 150 people, follows two other bombings this year in Hezbollah bastions in Beirut, amid rising tensions over the conflict in neighbouring Syria.
Iran is one of Syria's closest allies, and is the key sponsor of Hezbollah, a powerful Shiite movement that has dispatched thousands of fighters to bolster President Bashar al-Assad's regime in the 32-month uprising.
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