The Indonesian Foreign Minister says Australia's policy of turning back boats fails to meet international commitments.
Indonesia has already met with the Australian Ambassador in Jakarta over concerns.
However Foreign Minister Julie Bishop has told the ABC that Australia retains a sound relationship with Indonesia.
"If there's an issue that we know is coming up we'll contact our counterparts. We have open lines of communication and I am constantly talking to Dr Natalagawa (Indonesian Foreign Minister).
"I think he said recently that we talk almost every day. It's a very positive relationship.(But) of course we have challenges."
Opposition immigration spokesman Richard Marles says the calling in of Mr Moriarty is a sign of deteriorating bilateral relations.
"We should be working effectively together between Australia and Indonesia, the truth is we're in a period now where there is precious little cooperation at all," he told the ABC.
Earlier this month, Mr Natalegawa said Australia's policy of turning back asylum-seeker boats was "unhelpful" to improving relations between the two countries.
He made the comments after the Australian Government said it had entered Indonesian waters in error while trying to stop asylum seeker boats.
