The delegation, comprising eight clerics, congratulated Iraqi Muslims on the advent of Ramadan and stressed national unity among Iraqis.
The visit on Monday came after explosions damaged five churches in Baghdad on Saturday, in attacks apparently designed to strike fear into Iraq's small Christian community. A string of bloody church bombings in August killed 11 people.
During their meeting, the Muslim and Christian leaders vowed to work for a united, peaceful and independent Iraq.
The AMS in a statement on Sunday condemned the latest church attacks, but held the US "occupation" responsible for the unrest the country is suffering.
It accused "the enemies of Iraq" of plotting to sow the seeds of discord among its people.
The AMS was established after the US-led war on Iraq and aims to unify Muslim authorities in the country.
Based in Baghdad, it is regarded as one of the most influential Muslim authorities in Iraq. It has formed alliances with some Iraqi Shia Muslim authorities.
Patriarch Mar Emmanuel Dalli spoke on behalf of the Christian delegation, stressing the need for coordination among Iraq's religious bodies.
"Christian leaders in Iraq are in solidarity with their brothers in the Association of Muslim Scholars, and work with them side by side to secure the interests of Iraq and Iraqis," he said.
Muhammad Ayash, the AMS spokesman, told Aljazeera.net the history of Iraq proved it was nearly impossible to initiate a conflict among Iraqis.
"The history of Iraq shows that Iraq's religious and ethnic mosaic has lived in harmony across history. Diversity has been the miracle of Iraqi society. The brotherhood among Iraqis will remain intact no matter what the enemies of Iraq do," he said.
Christianity is Iraq's second major religion. It appeared in the country about 30 years after the ascension of Jesus.
Iraqi Christians are mainly Catholic and Nestorian. They make up about 2.7% of the population.
Between the 3rd and the 6th centuries, the Arab Christian kingdom of al-Manathera flourished in southern Iraq. Its capital al-Heera exists to this day and retains its original name.