The Assyrian Church of the East reads Matthew 16:18 as affirming that the Church is built on apostolic faith (the confession of Peter) and on the apostolic succession of bishops. The Church maintains the historic episcopate and claims apostolic succession from the apostles through its patriarchate. The 'rock' refers to Christ and to Peter's apostolic confession.

The Assyrian Church rejects Roman papal primacy and claims that its Catholicos-Patriarch stands in apostolic succession as the chief pastor, not as a universal pope. This reflects the ancient Eastern understanding of apostolic authority distributed among the ancient sees.