Indonesians have burned Australian flags over reports that Australian spies tried to tap the phones of President Susilo Bambang Yudhoyono and his wife.

About 200 people marched on Thursday to the heavily fortified Australian embassy in Jakarta to demand an apology over the alleged spying, which prompted Yudhoyono to downgrade diplomatic relations with Canberra a day earlier.

"We are ready for war with Australia," stated one of many banners carried by protesters.

Other protesters in the central Javanese city of Yogyakarta burned Australian flags in a show of anger, but the demonstrations were peaceful and smaller than police expected.

Australia earlier updated its travel advisory for Indonesia, the country's second most popular tourist destination after New Zealand, urging citizens in the Southeast Asian country to avoid protests and "maintain high levels of vigilance".

Yudhoyono appeared on national television on Wednesday to announce a freeze on military and intelligence cooperation, including over the controversial issue of asylum seekers.

Stirring the Indonesian outrage were reports quoting documents leaked by Edward Snowden, the former US National Security Agency contractor, suggesting Australia tried to monitor the phones of top Indonesian officials in 2009.

Regret expressed

Tony Abbott, the Australian prime minister, has not confirmed the spying or apologised, although he has expressed regret for the embarrassment the media reports caused to Yudhoyono and his family.

In a statement to parliament on Thursday, Abbott said he had received an official letter from Yudhoyono seeking an explanation for the spying reports and would respond "swiftly, fully and courteously".

Hatta Rajasa, Indonesia's coordinating minister for economic affairs, said the dispute had caused little economic impact.

"In the area of economy and business, our cooperation is continuing," he said.

Gita Wirjawan, trade minister, said Indonesia was reviewing its trade ties with Australia, worth more than $11bn last year.

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