Indonesia’s President Joko Widodo will fly to Australia this weekend, a trip seen as a high point in a often-tumultuous relationship that has gradually thawed since last year’s execution of two Australians.

The leader of the world’s most populous Muslim-majority nation, nicknamed Jokowi, will visit Sydney, for trade talks, and Canberra, where he will address parliament.

Bilateral relations between the two countries have suffered repeated hits and both sides have made efforts this year to fix them.

In 2013 it was revealed that Australia’s spy agencies had attempted to listen in on the personal phone calls of the then-president, Susilo Bambang Yudhoyono, and targeted the mobile phones of his wife.

And Indonesia was further frustrated that year after Canberra implemented a controversial policy of turning back boats of refugees. Several hundred asylum seekers continued to arrive in Indonesia each month, having previously used it as a stopover point, and there are now more than 14,000 people stuck there.

The issue festered again this March when a freedom of information request revealed Australian maritime patrols had pushed back boats into Indonesian territorial waters six times. Australia had to apologise to Indonesia for the unintentional breaches of its waters.

Diplomatic spats between the two countries have led to low levels of trade and Australian foreign direct investment into Indonesia is substantially less than to other countries that are geographically further away.

Jokowi’s trip will be heavily focused on trade deals, as well as security cooperation, and the president will be hoping to secure Australian investment for infrastructure projects.

Indonesia’s trade minister, Enggartiasto Lukita, said Australia had already made a request to pay the same sugar import tariff as Association of South-East Asian Nations (Asean) countries — at 5% compared with states outside the trade bloc. In return, Indonesia wanted to export biofuels at a set price, he added.

Australia is also seeking to secure assurances for exporting cattle to Indonesia, with sales to the south-east Asian country at well over AS$1bn a year. Indonesia had suggested that it might reduce its reliance on Australia.

The visit follows a trip by Australia’s prime minister, Malcom Turnbull, in November last year and another meeting he held with Jokowi in Laos on the side of this year’s Asean summit.

Both events were strong signals that Australia was still seeking to restore the relationship after the executions of Australian drug smugglers Andrew Chan and Myuran Sukumaran, which led Canberra to temporarily recall its ambassador.

“It’s no longer the time for fragile egos and thin-skinned national pride. It’s time to roll up our sleeves and see what we can do together,” the former Indonesian trade minister Thomas Trikasih Lembong said last month.

The two countries have also found common interests in the South China Sea, where Indonesia, as well as several other countries, have territorial disputes with China.

A joint statement released during a visit last month by Australia’s foreign minister, Julie Bishop, to Indonesia said the two countries were “natural maritime partners”.

And on Tuesday, Bishop went further by announcing Australia was considering joint naval patrols with Indonesia in the contested waters.

“This is a regular part of what our navy does,” Bishop said. “This is part of our engagement in the region and this is in accordance with Australia’s right of freedom of navigation including in the South China Sea.”

