David Bitan, the Likud party's parliamentary whip and a close Netanyahu ally, told Army Radio the vote set for Sunday is delayed because "there is American pressure claiming this is annexation."
He said it will take time to clarify the bill to the US.
The law stops short of annexing West Bank territory to Israel, and its practical implications are unclear.
It says the communities will be considered "daughter municipalities" of Jerusalem.
The international community is widely opposed to settlement construction. US President Donald Trump has urged restraint as his administration tries to restart Israeli- Palestinian peace talks.