Zebari, speaking to reporters in Saudi Arabia, said on June 18 that the request to Washington to bomb insurgents from the Islamic State of Iraq and the Levant (ISIL) was made under a bilateral-security agreement.
He said a request was made for the U.S. to "conduct air strikes against terrorist groups."
Zebari added that "a military approach will not be enough," saying that "drastic political solutions" are also needed.
The chairman of the U.S. Joint Chiefs of Staff, Martin Dempsey, confirmed receiving the request from the Iraqi government.
Dempsey did not say if the United States would launch airstrikes in Iraq but responded indirectly saying, "It is in our national security interest to counter ISIL wherever we find them."
U.S. Vice President Joe Biden spoke with key Iraqi leaders to urge unity against insurgents led by the ISIL.
Biden also stressed the need to form an inclusive government after national elections on April 30.
The White House said Biden spoke with Iraqi Prime Minister Nuri al-Maliki as well as Maliki's Sunni rival, parliamentary speaker Osama al-Nujaifi, and Masoud Barzani, the president of the Iraqi region of Kurdistan.
U.S. President Barack Obama briefed congressional leaders on June 18 on efforts to get Iraqi leaders to "set aside sectarian agendas," reviewed options for "increased security assistance" and sought their views.
Earlier, Nuri al-Maliki said that government forces are "regaining the initiative and striking back" after militants from an Al-Qaeda splinter group seized large swaths of territory in the north of the country.
In a televised address on June 18, Maliki, a Shi'ite, said the "shock" of the militants' advance in the mainly Sunni north has helped restore Iraq's national unity.
Maliki admitted the army had suffered a setback, but said that "not every setback is a defeat."
Militants spearheaded by the ISIL have seized the key cities of Mosul and Tikrit after launching their offensive earlier this month and pushing toward Baghdad.
Government forces on June 18 said they had regained parts of the strategic Shi'ite-majority town of Tal Afar near the Syrian border and repelled an attack on the oil refinery in Baiji, north of Baghdad.
The army said 40 militants were killed in fighting at Baiji, but the claim could not be independently confirmed.
Saudi Foreign Minister Prince Saud al-Faisal on June 18 said the deteriorating security situation in Iraq shows signs of a "civil war."
Iraq's government has accused Sunni Saudi Arabia of financing the militants.
Iranian President Hassan Rohani on June 18 said his country, Saudi Arabia's regional rival, would do whatever it takes to protect Shi'ite holy sites in Iraq against the Sunni militants.
India's Foreign Ministry, meanwhile, said 40 Indian construction workers have been abducted near the northern city of Mosul.
Turkish media reports said 60 foreign construction workers, including some 15 Turks, were reported abducted by ISIL militants near the northern oil city of Kirkuk.
Last week, 80 Turkish nationals were seized near Mosul, 49 of them from the Turkish consulate in the city.
U.S. President Barack Obama is considering military options to push back the ISIL. But in return Washington wants Maliki to address concerns of the minority Sunnis, which ISIL has exploited to win support.
Obama announced on June 16 that some 275 U.S. soldiers would be available to protect the American Embassy in Baghdad.