The Coalition and Labor have agreed to cut back a baby bonus payment worth $367 million as part of the deal to pass the $6.3 billion omnibus savings bill, which will also water down proposed cuts to renewable energy funding and preserve the clean energy supplement for "vulnerable" recipients.

As the Coalition party room continued to grapple with the details of the same-sex marriage plebiscite, Labor was first to announce the compromised legislation, with shadow treasurer Chris Bowen saying both sides had worked together in the national interest.

The baby bonus payment, which formed a key element of the Coalition power-sharing agreement struck by Prime Minister Malcolm Turnbull and Nationals leader Barnaby Joyce in September 2015, would have given eligible families with a youngest child under one year an extra $1000 a year through an increase to their Family Tax Benefit part B payment.

The clean energy supplement will not be abolished - which would have saved $1.3 billion - for most new recipients of welfare payments. There had been intense pressure from welfare groups and internally from Labor's left faction to block this cut.