Principals would also be able to keep any savings to invest in other projects.
"I trust the school communities," Mr Abbott told reporters after a tour of Annangrove Public School in Sydney on Wednesday.
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"I am confident that school communities of Australia and the principals of Australia will do the right thing by their kids."
Mr Abbott said principals should be able to decide themselves on how to spend any leftover money after planned construction is complete.
"We trust the principals with our kids' futures. Why can't we trust them to manage taxpayers' dollars?" he said.
Most government schools would be able to save about a third of their total funding by self-managing projects, Mr Abbott said, adding that if the Liberal-led coalition wins government at the next election, it will free up the funds during its first week in power.
The federal government is spending $16 billion on school facilities to stimulate the economy, but critics accuse the BER program of wasting money and being prone to rorting.
