The Gambian government announced last week that the former British colony was pulling out of the Commonwealth with immediate effect, saying it would "never be a member of any neo-colonial institution".
The announcement stunned the organisation, with Commonwealth secretary-general Kamalesh Sharma expressing his "dismay and disappointment".
Abbott, who supports retaining Australia's links to the British monarchy, said: "I do think the Commonwealth is an important forum.
It's amongst our oldest international associations.
"There is, I suppose, familiarity amongst members of the Commonwealth which doesn't always exist in every other forum and I think it's important that those friends we have, we should keep," he said.
"You do not make new friends by rubbishing your old friends or abandoning your old friends," Abbott added, vowing that his government would "take the Commonwealth seriously". Conservative leader Tony Abbott indicated disagreement with Canadian Prime Minister Stephen Harper,