During the meeting in Baghdad on Wednesday, Anad appreciated Iran's efforts in fighting terrorism.
He said Iraq is ready to promote cooperation with Iran.
Masjedi, for his part, congratulated Anad for his election as defense minister of Iraq.
He also underlined Iran's readiness for developing relations with Iraq.
The Iranian ambassador noted that no efforts will be spared in line with having a powerful Iraq.
Earlier this month, Iranian President Hassan Rouhani said stability in Iraq is important, and stressed the need to boost Tehran-Baghdad ties.
In his phone conversation with Iraqi President Barham Salih, Rouhani discussed regional developments and underlined strengthening of Tehran-Baghdad relations.
Today, the regional countries are facing many problems, he said, adding, "Bolstering all-out relations and cooperation between friends can be a way to overcome problems."
"The Islamic Republic of Iran stands by the Iraqi government and nation like before, and favors protecting Iraqi sovereignty and non-interference of foreign powers in the future of the country’s government and people," he noted.
Iraqi president, for his part, congratulated the arrival of Eid al-Fitr in advance, stressing the need for further development of relations and cooperation between the two countries.
Referring to the importance of Iran-Iraq political relations, he said, "The stability and security of Iraq require cooperation between friendly and neighboring countries, especially with the Islamic Republic of Iran."
Referring to the destructive interference of foreign powers in the region, Salih said, "The Middle East cannot tolerate new crises; thus, the interference of foreigners in the region must end rapidly."