The Abbott government is pushing ahead with a religious-only school chaplaincy scheme following a cabinet debate over whether secular welfare workers should be included in the program.

The government was forced to redesign the $244 million scheme after the High Court ruled it invalid in June for the second time in two years. The court found the Commonwealth had over-reached its funding powers by providing direct payments to chaplain providers.

In a bid to prevent another High Court challenge, the federal government will provide funding to state and territory governments to administer the scheme. This new arrangement strengthens the hand of the states and could see some demand an option for secular welfare workers or tougher qualification standards.

In a cabinet meeting on Monday, Abbott government ministers explored options to extend the scheme to include funding for secular welfare workers. This would have reversed the government's existing policy that funding should be restricted to religious chaplains. During the cabinet discussion, Mr Abbott argued that the government should stand by its existing policy. Mr Abbott argued the scheme's original intent was supporting pastoral care in schools and that should remain its focus. The chaplaincy scheme was also raised in the Coalition party room on Tuesday, where at least two government members argued the scheme should be broadened to include funding for secular workers.