The volatile country, one of the world's leading state sponsors of terrorism, would also likely sell or give nuclear weapons to extremist groups that consider America an enemy, they said.
"For the world's most dangerous regime to obtain the world's most dangerous weapons is something that neither the United States nor the community of civilised nations can allow," the leaders assert.
Among the prominent leaders to sign the letter were Pat Robertson, president of Christian Broadcasting Network, Charles Colson, chairman of Prison Fellowship Ministries, Johnny Hunt, current president of the Southern Baptist Convention, and John Hagee, senior pastor of Cornerstone Church in San Antonio, Texas.
Former SBC presidents, a representative from Focus on the Family, and presidents of Christian universities were among the signatories.
They hope that government leaders meeting in Pittsburgh for the G20 summit will take coordinated efforts against Iran.
Tough actions proposed include a total arms embargo and a halt to exports of refined petroleum products, including gasoline, from Iran. The economic sanctions would also apply to foreign companies that export, ship, finance or broker refined petroleum products to Iran.
Christian leaders noted that though Iran has large oil reserves, it is unable to refine its petroleum products and is vulnerable to such sanctions.
Israeli Prime Minister Benjamin Netanyahu concurred with the Christian leaders, saying that if Iran obtained nuclear weapons it could "bring terrorism beyond our wildest dreams", in an interview on NBC's Today show on Wednesday.
Netanyahu said that if the UN Security Council did not respond to the problem, then leading nations could pressure Tehran with tactics such as importing petroleum products.
Iran, however, claims its nuclear programme is for peaceful purposes.