Prime Minister Tony Abbott says he’s encouraged by the Indonesian president’s remarks following the spying revelations, even if serious issues persist.

Prime Minister Tony Abbott has repeated his “deep and sincere” regret over recent spy allegations, after Indonesian announced it had suspended all military cooperation with Australia.

Mr Abbott sought leave in the parliament to respond to the deepening diplomatic crisis, after Indonesian president Susilo Bambang Yudhoyono requested an official apology and a full explanation as to why Australian spies targeted his mobile phone in 2009.

The prime minister said he was “encouraged” by the President’s remarks about the strength of the bilateral relationship between Australia and Indonesia.

“Although obviously there are very seriously issues that do need to be worked through in the near future between us,” he told the House of Representatives on Wednesday.

“I want to express here in this chamber, my deep and sincere regret about the embarrassment to the president and to Indonesia that’s been caused by recent media reporting.”

The president has indicated that he would shortly be writing to Mr Abbott.

“I’d like to reassure the house that I will be responding to the president’s letter swiftly, fully and courteously,” Mr Abbott said.

“As always, I am absolutely committed to building the closest possible relationship with Indonesia because that is overwhelmingly in the interest of both our countries.”

Opposition leader Bill Shorten also spoke, telling parliament Labor would support the government’s efforts to rebuild the relationship.

“We do not underestimate the seriousness of this matter, or the sense of offence that our Indonesian friends are feeling,” Mr Shorten said.

“This is indeed a Team Australia moment. This is something that has happened to both Indonesia and Australia.

“We need to walk this road together. Other nations have resolved these similar issues. We can too.”