The details of the co-operation will form part of an updated strategic agreement set to be signed in 2025.
"This is a very significant step forward in what is already a broad and unique relationship," Australian Defence Minister Richard Marles said during a joint media conference in Singapore on Tuesday.
"We operate through the main air base and naval base here in Singapore and we want to look at ways in which we can increase the tempo of visits of both our navy and our air force."
Further training opportunities for Singaporeans in Australia were being worked on, he said.
Every Singaporean Air Force pilot has been trained in Australia.
"It says something about how close our defence forces are and we want to make that closer," Mr Marles said.
Australia will contribute $75 million for a Singaporean program to support the move to net zero in the region, Trade Minister Don Farrell said.
It's the first cash out the door from Australia's $2 billion Southeast Asia Investment Financing Facility.
Carbon capture and storage at Australia sites was discussed, Singaporean Trade Minister Gan Kim Yong said.
An underwater cable from Darwin in Northern Australia to Singapore to transport solar energy was also raised.
Australia was reviewing the project to see whether it could work after Singapore provided the necessary regulatory approvals, Mr Marles said.
"If it can, it really would be a significant step forward in the ability for us to effectively export our renewable energy," he said.
Australia and Singapore's defence, foreign affairs and trade ministers met for the annual 3+3 dialogue.
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