"I do understand how personally hurtful these allegations have been, these reports have been, for him and his family," he said.
"My intention, notwithstanding the difficulties of these days, is to do everything I reasonably can to help to build and strengthen the relationship with Indonesia which is so important to both our countries," he added.
But Abbott failed to directly answer a question asked by opposition leader Bill Shorten: What progress had been made to restore Australia's relationship with Indonesia?
Analysts describe the furor as the lowest point in a perennially volatile bilateral relationship since 1999, when Australia led a U.N. military force into the former Indonesian province of East Timor following a bloody independence ballot. At that time, Indonesia ripped up a 4-year-old security treaty with Australia. A new treaty has since been signed.
Indonesian Religious Affairs Minister Suryadharma Ali has become the first government minister known to have canceled a visit to Australia because of the spying furor, an Australian academic said on Wednesday.
Prof. Damien Kingsbury, director of Deakin University's Center for Citizenship, Development and Human Rights, said Ali was to arrive in Melbourne next weekend to give a seminar on managing religious diversity in Indonesia.
Ali canceled on Tuesday, said Kingsbury, who had organized the seminar based on Ali's promise to attend.
"The technical reason given in writing in the official letter was that he had to resolve some financial matters to do with his party before the end of the year," Kingsbury said.
"But the email correspondence I got from his office was that it was obviously too sensitive; it was too difficult a time for him to come," he said.
The minister could not immediately be contacted for comment.
Abbott told Parliament on Tuesday he would not apologize or explain Australia's espionage activities.
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Kotarumalos reported from Jakarta, Indonesia.