* Emergency EU summit on Russia could be held next week
* Sanctions threat extended, but EU wants to give diplomacy a chance
* EU looks at possible police mission to Ukraine
* Four Ukrainians added to sanctions list (Releads with Fabius)
By Justyna Pawlak and Adrian Croft
LUXEMBOURG, April 14 (Reuters) - The European Union could hold an emergency summit next week to impose further sanctions against Russia if there is no breakthrough at talks with Ukraine scheduled for Thursday in Geneva, France's foreign minister said on Monday.
At a meeting in Luxembourg, several EU foreign ministers threatened Moscow with new sanctions over its actions in eastern Ukraine, although some said diplomacy should be given time before firm decisions are taken.
France's Laurent Fabius said he hoped "fundamental questions" about Ukraine would be tackled at Thursday's meeting involving Russia, Ukraine, the United States and the EU.
"If it is necessary, there may be a meeting of heads of state and government next week at European level, which may adopt new sanctions," he told reporters.
"The goal is to show firmness while keeping a dialogue open," he said.
Ukraine dominated Monday's talks among EU foreign ministers after Kiev threatened military action against pro-Russian separatists occupying government buildings in the east.
British Foreign Secretary William Hague, arriving for the meeting in Luxembourg, said there could be no doubt that Moscow was behind the destabilisation of eastern Ukraine.
"I don't think denials of Russian involvement have a shred of credibility," Hague told reporters, adding that the EU now needed to discuss adding more people to a list of 33 Russian and Ukrainian officials targeted by EU asset freezes and travel bans over the Ukraine crisis.
Polish Foreign Minister Radoslaw Sikorski said the EU must now agree how the list could be expanded.
"The EU has to make it clear to Russia what are the consequences of any possible future actions in eastern Ukraine," he said. "I expect a very specific signal when we can expect sanctions if Russia takes further steps."
But other governments were more cautious on sanctions, underscoring concerns in parts of Europe about antagonising a power with an energy stranglehold over the bloc, and put their faith in Thursday's talks.
Germany said the Geneva meeting could help calm tensions even though the option of sanctions remained on the table.
In addition to widening asset freezes and visa bans, the EU is discussing possible more far-reaching measures, such as restrictions on trade and finance with Russia, which Hague said should be prepared quickly.
Jean Asselborn, Luxembourg's foreign minister, said sanctions wouldn't "resolve the problem".
"Our main task today is to do everything so that this conference on Thursday in Geneva can take place and take place in a calm atmosphere," he said.
The ministers agreed some steps to help Ukraine overcome its deepening economic crisis, approving a package of nearly 500 million euros ($685 million) worth of trade benefits, which include the removal of duties on a wide range of agricultural goods, textiles and other imports.
Four Ukrainians were also added to a list of people targeted with EU sanctions over misappropriation of state funds.
Under discussion on Monday was also a possible EU mission to train police and other law-enforcement officials in Ukraine to help stabilise the country, as proposed by Britain, Sweden and Poland, and supported by Germany.
Such a mission - likely to irritate Russia - would seek to rebuild Ukraine's police and legal system in the short term to help combat violence in the country of 46 million people and lay the groundwork for implementing a proposed free-trade deal with the European Union.
The bloc will also discuss its approach to issuing visas and trade with the Crimean peninsula, which was annexed by Moscow in March after popular protests toppled pro-Russian president Viktor Yanukovich in Kiev.
"It is important to show that there won't be a recognition of the annexation through the back door," said one diplomat. (additional reporting by Tom Koerkemeier, Luke Baker and Barbara Lewis in Brussels; editing by Giles Elgood and Philippa Fletcher)