Prime Minister Scott Morrison has stripped leadership rival Peter Dutton of his immigration responsibilities and taken control of the population debate as a top economic priority.

Mr Dutton was handed back a weakened Home Affairs portfolio on Sunday, following his failed conservative rebellion against former prime minister Malcolm Turnbull.

But in a sign of how seriously he is taking the political threat of the immigration debate, Mr Morrison has restored immigration as a standalone ministry under moderate David Coleman and bolstered it with another ministerial position: cities, urban infrastructure and population, to be handled by Dutton-ally, Alan Tudge.

The conservative push against former prime minister Malcolm Turnbull was fuelled by a divisive immigration debate, which has seen sustained economic growth at the same time as infrastructure has groaned under its weight.