Australian Prime Minister Tony Abbott says his response to the Indonesian president's angry letter seeking explanation following reports of Australian phone tapping of Indonesian leaders is on its way to Jakarta.

Australians are hoping that Abbott's quickly crafted letter will quell Indonesian anger over National Security Agency fugitive Edward Snowden's leaked documents that show Australia bugged the phones of President Susilo Bambang Yudhoyono, his wife and eight Indonesian ministers and officials in 2009.

A furious Yudhoyono recalled Indonesia's ambassador, downgraded relations with Australia and wrote to Abbott demanding an explanation.

Abbott told reporters on Saturday he had written the response which "is now in the process of being delivered."

Abbott declined to say what he had written but added he wanted to ensure the relationship "goes from strength to strength."