By Karen Lema and Martin Petty

MANILA (Reuters) - The Philippines has turned down a Chinese proposal to start bilateral talks on their South China Sea dispute, its foreign minister said on Tuesday, because of Beijing's pre-condition of not discussing a court ruling that nullified most of its claims.

China claims most of the South China Sea, through which more than $5 trillion of trade moves annually. Brunei, Malaysia, the Philippines, Taiwan and Vietnam have rival claims.

Perfecto Yasay said he had met his Chinese counterpart Wang Yi on the sidelines of a meeting of Asian and European leaders in Mongolia at the weekend and after raising the topic of last week's ruling, it became clear that was a no-go area.

China's foreign ministry said in a statement Tuesday night that the two ministers had "informal contact" in Mongolia.

Wang said if the Philippines was willing to resume talks, manage divisions and improve relations, China would meet it halfway, according to the statement.

China has angrily rejected the verdict by the Permanent Court of Arbitration in The Hague and the initial case as illegal and farcical. It has repeatedly said it will not change its approach or its sovereignty claims in the South China Sea.

"They said if you will insist on the ruling, discussing it along those lines, then we might be headed for a confrontation," Yasay said during an interview with the news channel of broadcaster ABS-CBN.

"But I really honestly feel that this is something they have to make on a public basis but I also sensed there was room for us to talk very quietly using backdoor channeling."

Yasay said Wang had proposed bilateral talks but only on issues "outside, or (in) disregard of, the arbitral ruling", which he declined because it was not in the Philippines' national interests.

The Chinese foreign ministry's account of Wang's remarks struck a more conciliatory tone and did not mention pre-conditions.

"Promoting a return to dialogue in China-Philippine relations is in the fundamental interests of the two countries and their people," the statement said Wang emphasized.

Yasay's account of the meeting highlights the challenge ahead for the Philippines, a U.S. ally, in getting China to comply with the decision which has ramped up tensions in the vital trade route.

The ruling laid out what maritime rights Manila had and where Beijing had violated its rights under international law, including its massive construction works on Mischief Reef.

Manila wanted to enforce the points of the complex ruling step-by-step but as a priority had asked China to let its fishermen go to the contested Scarborough Shoal without being harassed by its coastguard, Yasay said.

China's coastguard was preventing Filipino boats from fishing around Scarborough Shoal, fishermen and officials said on Friday, and China's air force has released pictures showing bombers recently flying over the area.

(Reporting by Karen Lema and Martin Petty; Additional reporting by Ben Blanchard in BEIJING; Editing by Lincoln Feast)