JAKARTA (REUTERS) - Indonesia's President Joko Widodo on Friday (Jan 10) asked Japan to step up investment in fisheries and energy in some of its South China Sea islands, following a stand-off with China in waters that China claims in the area.

Mr Joko made the request for Japan to consider economic opportunities in the Natuna islands during a visit to Jakarta by Japanese Foreign Minister Toshimitsu Motegi, the president's office said in a statement.

"I want to invite Japan to invest in Natuna," he told Mr Motegi, adding that Japan was one of Indonesia's major economic partners.

Mr Joko visited Natuna on Wednesday to assert Indonesia's sovereignty over the cluster of islands and the waters around them, after reports that Chinese coastguard and fishing vessels had entered Indonesia's exclusive economic zone several times since last month.

China has not claimed the Natuna islands themselves but says it has nearby fishing rights within a self-proclaimed Nine-Dash Line - a line on Chinese maps that it says shows its territory and waters.

The line loops far south from China and includes most of the South China Sea, but it is a claim that is not recognised internationally. Vietnam, the Philippines, Brunei, Malaysia and Taiwan have rival claims in the South China Sea.

Indonesian Foreign Minister Retno Marsudi told reporters Mr Joko had asked Japan to invest in fisheries, energy and tourism in Natuna. "We also agreed to strengthen coastguard coordination," he said.

Indonesia had stepped up air and sea patrols in the area and summoned China's ambassador over the appearance of the ships. An Indonesian military spokesman said the vessels left the area after Mr Joko's trip.

China says it is in contact with Indonesia through diplomatic channels to resolve differences and uphold stability in the region.

Mr Motegi, speaking through a translator after a meeting with Ms Retno, did not refer to China but said Japan was wary about the situation in the South China.

"We shared a serious concern regarding efforts to change with force the status quo unilaterally and we confirmed continuing close collaboration," he said.

Japan last year gave Indonesia 100 billion rupiah (S$9.8 million) to build a fish market in Natuna, which will be named Tsukiji after the famous Tokyo market, media reported.

Construction of the market in Natuna and markets on other Indonesian islands will begin this year, Mr Motegi said.