The Turnbull government has dumped one of the most controversial measures in the Coalition's politically toxic 2014 budget – the full deregulation of university fees – but opened the door to other potentially unpopular changes such as a new two-tiered fee system.

Education Minister Simon Birmingham shelved the plan to allow universities to set their own fees late last year, but has now officially consigned the policy to the scrap heap following an effective "$100,000 degree" scare campaign by the Labor opposition.

The government, which had already announced a $1.2 billion boost for school funding, hopes the backdown will allow it to neutralise education funding as a policy battleground in the upcoming federal election.