INDONESIA'S Ambassador to Australia has called for relations to be rebuilt between the two countries after two Australians were executed by Indonesian authorities this week.

The execution of Bali Nine drug smugglers Andrew Chan and Myuran Sukumaran this week has renewed tensions between the countries and sparked a call for a new discussion on the death penalty.

But a statement from Ambassador Nadjib Riphat Kesoema called for both parties to overcome the "challenging period" and "rebuild this important bilateral relationship".

Mr Kesoema also expressed his sympathies to Chan and Sukumaran's families, despite Australian leaders expressing concerns about their treatment while in Indonesia for the executions.

The ambassador wrote that good relations were beneficial for both nations, and Jakarta remained "strongly committed" to improve the tense relationship.

But the statement followed Foreign Minister Julie Bishop's call for wider regional talks about the use of the death penalty for drug offences.

Mr Kesoema did not respond to Ms Bishop's urging, instead writing Indonesia understood "the views expressed".

He wrote the penalty came from a court case, rather than President Joko Widodo's office.

This was despite Mr Widodo repeatedly refusing to act on the government's calls for mercy for the pair.