Critics say the law would institutionalize long-running constraints to the building of churches in the Muslim-majority country.
For decades, church officials have had to navigate Egypt's labyrinthine bureaucracy to acquire permits for the building of new churches. They have also faced pressure from security agencies that fear churches could become flashpoints for sectarian unrest.
The MENA agency quoted parliament speaker Ali Abdel Aal as saying at the end of Tuesday's session that two thirds of the 596-member House of Representatives, mostly loyalists of President Abdel-Fattah el-Sissi, voted in favor of the law.
Earlier sessions saw Coptic lawmakers shout down the proposed legislation.