GENEVA, June 12 (Reuters) - Turkey told the World Trade Organization on Wednesday that it would retaliate against a Ukrainian tariff on car imports, while Japan and the European Union signalled they could follow suit.

Turkey's retaliation was tiny in global trade terms, amounting to a 23 percent tax on Ukrainian walnuts which Turkey estimates will raise $6.1 million, equivalent to the damage done to Turkey's car exports by Ukraine's tax.

But it amounts to a warning shot for Ukraine, signalling that other disgruntled WTO members may take similar action - and any future retaliation would hurt much more than Turkey's measure.

"If we don't act we risk losing our rights. We may retaliate," one EU official said.

The European Union, Japan, South Korea and Russia are all car exporters to Ukraine and have demanded an explanation for the tax, which came into force in March for three years.

Under the WTO rules, member countries can impose "safeguard" tariffs to protect a sector if there is a threat of serious damage to producers from a surge in imports. But there are strict rules about their use, which Ukraine is accused of ignoring.

"Countries are clearly looking at next steps as Ukraine is not cooperating or upholding the safeguard agreement," the EU official said.

Diplomats say the car tariff is part of a pattern of aggressive and eccentric behaviour by Ukraine, which is vetoing Yemen from joining the WTO, pursuing a legal challenge to Australian tobacco laws and undermining the WTO system by demanding a far-reaching renegotiation of its tariffs.

Ukraine's critics say it had no grounds to use safeguards, should have given prior warning that it was thinking of doing so, and did not give car exporters a chance to negotiate equivalent "payment" in some other sector, as it should have.

In a filing to the WTO, Japan said it had requested a meeting with Ukraine, but there was no response, at least until it was too late and the tariff was already in force. Japan and other WTO members asked for the meeting to take place in Geneva, but Ukraine wanted it in Kiev, without specifying a date.

"This unilateral imposition of additional duties is clearly inconsistent with the relevant WTO agreements. Japan reiterates its request to Ukraine that it immediately terminate this unjustifiable imposition of additional duties," said Japan's notification, published on the WTO website on Wednesday.

"In the event of Ukraine's failure to do so, Japan will consider taking necessary steps under the WTO agreements."

Japan did not specify what sanctions it might use, as Turkey did, but notified the WTO's Council on the Trade in Goods of Ukraine's breach of the rules. The Council meets on July 11 and is set to rubber-stamp Turkey's retaliation, which comes into force the following day.

The EU official said the five complainants were cooperating in their challenge against Ukraine.