* Russia sets conditions for meeting on Ukraine
* Says Kiev government must not ignore east and south
* EU establishes support group for Ukraine (Adds Russia says Kerry and Lavrov hold second conversation)
By Steve Gutterman and Adrian Croft
MOSCOW/BRUSSELS, April 9 (Reuters) - Russia told the West on Wednesday that four-way talks between representatives of Ukraine, Russia, the United States and European Union must focus on fostering dialogue among Ukrainians and not on bilateral relations among the participants.
Foreign Minister Sergei Lavrov delivered the message in a telephone conversation with U.S. Secretary of State John Kerry, the Foreign Ministry said. It said Lavrov and Kerry urged all sides to refrain from violence in eastern and southern Ukraine.
The European Union said on Tuesday that top diplomats from the EU, Russia, Ukraine and the United States would meet next week to discuss the crisis, but Russia says it wants to know more about the agenda for such a meeting.
"Lavrov noted that this format could be useful if it is aimed not at discussing various aspects of one bilateral relationship or another, but on helping to arrange a broad and equal internal Ukrainian dialogue with the aim of agreeing mutually acceptable constitutional reform," the ministry said.
Russia, which made Ukraine and the West furious by annexing Crimea last month, does not want to be forced into talks with the interim government in Kiev because of that administration's role in ousting Moscow-allied President Viktor Yanukovich in what Moscow called an armed, Western-encouraged coup.
Russia accuses the government of ignoring the rights and interests of Russian speakers in the east and south Ukraine and is calling for a new constitution that would grant the regions strong powers and keep Ukraine out of NATO.
Lavrov told Kerry "the authorities in Kiev must finally respond to the legitimate demands of eastern and southern regions of the country," the ministry said.
Later, the ministry said Kerry had telephoned Lavrov again and told him the United States was urging Ukraine's government to organise nationwide dialogue to ease tension in the east and south of the country and promote constitutional reform.
Lavrov told Kerry that "progress toward those ends will support" efforts to hold a four-way meeting, the ministry said.
Kerry on Tuesday accused Russian agents and special forces of stirring up separatist unrest in eastern Ukraine.
The crisis in Ukraine erupted after Yanukovich cancelled plans to sign trade and political pacts with the EU in November and instead sought closer ties with Russia, triggering protests that turned bloody and drove him from power.
Moscow annexed Crimea in March following a referendum staged after Russian forces established control over the Black Sea peninsula in the biggest East-West crisis since the Cold War.
On Wednesday, the EU created a dedicated support group to advise Ukraine on political and economic reforms and coordinate with other donors and international lenders.
The Brussels-based group is intended to channel EU help and advice for Ukraine through a single coordinating body, and underlines EU support for the new government, which is trying to stabilise the economy while tensions with Moscow remain high.
NATO says Russia has massed tens of thousands of troops close to their Ukraine border.
"It is important to have this support for the ... political and economic reforms Ukraine needs to become a sustainable, independent, modern country," European Commission President Jose Manuel Barroso said in a statement.
Last month, the EU said it was willing to provide $15 billion in loans and grants to Ukraine over the next several years. The International Monetary Fund announced a $14-$18 billion loan for Kiev in return for tough economic reforms.
The European Union and Ukraine signed a landmark political cooperation accord last month, committing to the same deal that Yanukovich rejected in November.
Although the free trade parts of the agreement will only be signed after Ukraine's May 25 presidential election, the European Commission has already agreed to extend trade benefits worth nearly 500 million euros ($689 million), removing duties on a range of farm goods, textiles and other imports.
The support group's work could be extended to Georgia and Moldova, which are also seeking closer ties with the EU. (Editing by Andrew Heavens)