Labor has revealed that its higher education policy would cost the budget nearly $14bn over the next decade, arguing there was “more than enough headroom” within its already announced savings measures to offset the spending.

The Labor leader, Bill Shorten, has been travelling around Australia this week promoting his plan to increase public funding for degrees and encourage universities to improve completion rates.

The pitch is designed to contrast with the Coalition’s stalled plan to deregulate university fees and reduce public funding for bachelor degrees, a proposal the government has indicated it will now rethink following Malcolm Turnbull’s elevation to the prime ministership.

“I truly believe Labor’s policies are the best way forward and we call upon Malcolm Turnbull to adopt the Labor policy of making it easier to go to university for smart kids not harder,” Shorten said during a visit to the Queensland University of Technology on Wednesday.

The policy has been estimated by the parliamentary budget office as costing $2.5bn in net terms over four years, compared with the existing budget papers that take into account the Coalition’s stalled savings measures.

Labor’s higher education spokesman, Kim Carr, revealed a longer term costing to Guardian Australia, saying the net amount between now and 2026 was $13.8bn compared with the budget papers.

“We think this is a reasonable, sustainable investment in building the skills base we need to create and support the jobs of the future,” he said.

“The additional expenditure will be offset, over the forward estimates and the medium term, by existing commitments to reform the taxation of multinational entities and superannuation tax concessions, and the abolition of the emissions reduction fund.

“These savings measures will deliver more than $21bn to the budget bottom line over the medium term.”

Carr said other measures previously funded from these savings measures included Shorten’s budget reply announcements on science, technology, engineering and mathematics; Labor’s response to domestic violence; the increase in humanitarian intake and additional funding for the UN refugee agency.

“There is therefore more than enough headroom without our announced savings to cover the net cost of the higher education package,” he said.

“But we should also recognise that the Liberals have so far completely failed to get any of their funding cuts through the Senate, so you can judge for yourself the reality of their budget position.”

Labor argues that in 2018 its “student funding guarantee” would provide $11,805 per student, or 28% more than would be the case under the Coalition’s policy settings. By 2026 the gap between funding under the two policies would have risen to 45%.

The opposition also argues that its funding commitments are based on the government’s own annual growth figures on commonwealth-supported places, indicating it is not budgeting for slower growth in student numbers.

University leaders had raised concerns earlier this year when Labor hinted it could be looking to curb the demand-driven system introduced by the former Gillard government, which removed caps on bachelor degree places and allowed funding for as many students as institutions enrol. They have welcomed the declaration that Labor would retain the demand-driven system.

However, Labor is looking at measures to encourage universities to improve course quality, accountability and completion rates – a push that might prompt universities to enrol fewer students than they otherwise would have. “We want more students to succeed,” Carr said.

The new education minister, Simon Birmingham, said on Monday he believed Labor’s scheme was “short on details”, and policy makers needed to be “very cautious” about incentives to increase completions because of the risk universities could adopt more discriminatory enrolment practices or engage in softer marking.