(Adds Australian agriculture minister postponing visit, reaction)

By Yayat Supriyatna and Kanupriya Kapoor

JAKARTA, Nov 23 (Reuters) - Rising diplomatic tension between Australia and Indonesia spread into the corporate world on Friday when a state-owned Indonesian firm suspended talks with Australian cattle farmers, citing trust issues between the neighbours.

Protests continued in Jakarta, where dozens of people burned Australian flags and images of Prime Minister Tony Abbott outside the heavily fortified Australian embassy in Jakarta. They demanded an apology over reports that Canberra had spied on President Susilo Bambang Yudhoyono and his wife.

The alleged spying prompted Yudhoyono to downgrade diplomatic ties with Canberra.

Australian Agriculture Minister Barnaby Joyce said on Saturday he was postponing a planned trip to Indonesia next week due to the row.

PT Rajawali Nusantara Indonesia (RNI) is the first Indonesian firm to freeze business ties with Australia due to the spying uproar.

"We decided to halt talks on cattle ranches in Australia temporarily until the Australian government fulfils what the Indonesian government insists they do," RNI Chief Executive Ismed Hasan Putro told Reuters.

"This is very important to build out mutual trust, respect and equality in the future."

Australia's Joyce said such a decision was for the company to make. "As minister for agriculture I support foreign investment when it is in the national interest. It is a matter for individual companies to make decisions about investment options as they arise," he said in a statement.

Putro, who declined to name the Australian companies, said RNI had already started talks with a New Zealand firm as an alternative candidate.

In September, RNI said it had sent a team to Australia to explore the possibility of investing around 350 billion rupiah ($29.91 million) in three or four existing cattle ranches, with the aim of importing 120,000 live animals a year.

Indonesian officials said on Wednesday the country was reviewing trade ties with Australia, worth more than $11 billion last year, but that beef and cattle imports had not yet been hit.

Indonesia is a major importer of Australian agricultural products such as wheat and live cattle, while Australia is Indonesia's 10th-biggest export market.

"Indonesia must take a firm stance with Australia as a country ... but business must not be mixed with politics," State-owned Enterprises Minister Dahlan Iskan told reporters.

SHUTTING DOWN

Yudhoyono said on national television on Wednesday that he was freezing military and intelligence cooperation, including on the issue of asylum seekers, a perennial irritant in relations.