* Cheney appeals to Ukraine to unite

* Russia criticises Cheney visit

* EU says plans "practically ready" for its Georgia mission

* Russia's allies fail to back Moscow fully on Georgia moves

By Tabassum Zakaria

KIEV, Sept 5 (Reuters) - U.S. Vice President Dick Cheney appealed to Ukraine's divided leaders on Friday to unite and forge closer links with the West, pledging Washington's support for Kiev to join the NATO military alliance.

Cheney was visiting amid a political crisis in Ukraine which has split the ruling coalition and sparked fresh debate about whether the former Soviet republic should draw closer to the West, to Russia, or pursue a neutral stance.

"The United States has a deep and abiding interest in your well-being and security," Cheney said after meeting President Viktor Yushchenko, a pro-Western leader seeking rapid NATO membership.

Ukraine's best hope to overcome threats, he added, "is to be united, united domestically first and foremost, and united with other democracies."

The vice president later visited a memorial to victims of a devastating famine in the 1930s, triggered after Soviet ruler Josef Stalin forced peasants into collective farms.

Cheney's visit was likely to anger neighbouring Russia, already irritated at his strong support on Thursday for Georgian membership of NATO. Moscow wants to keep Ukraine, a key gas transit country, part of its sphere of influence.

A Russian Foreign Ministry spokesman attacked Cheney for making fresh promises to Georgia on Thursday about NATO membership, saying this encouraged Georgian aggression.

Russia and Georgia fought a brief war last month after Tbilisi sent in troops to try to seize back the rebel region of South Ossetia, provoking massive retaliation by Moscow.

"The new promises to Tbilisi relating to the speedy membership of NATO simply strengthen the (President Mikheil) Saakashvili regime's dangerous feeling of impunity and encourages its dangerous ambitions," Russian Foreign Ministry spokesman Andrei Nesterenko told reporters.

The conflict has hurt Russian stocks and the rouble as foreign investors pull money out because of the increased political risk. Russian shares plunged more than 7 percent on Friday to their lowest level in over two years and the Central Bank intervened on Thursday to prop up the rouble.

DISSENT ON NATO

Yushchenko, hosting Cheney on Friday, said NATO membership was vital to protect his country, which shares a land border with Russia and has a large Russian-speaking population.

Cheney restated a promise made by NATO at a summit in Bucharest that Ukraine would be eventually allowed to join the military alliance, saying "that commitment stands today".

That meeting refused to give Kiev and Tbilisi a Membership Action Plan -- a first step towards membership. The U.S.-backed idea was resisted by Germany, France and smaller NATO states.

Nor is the idea of membership wholeheartedly embraced in Ukraine itself. Polls show a majority of Ukrainians oppose NATO membership and the leader of the country's biggest parliamentary party said the issue should be decided by the Ukrainian people.

"Any attempts to force Ukraine into NATO are doomed to failure," Viktor Yanukovich told a news conference. "This question has to be solved ... through a referendum".

Cheney was touring the region to show Washington's support for Ukraine, for close U.S. ally Georgia and also for booming oil state Azerbaijan.

The latter two countries are key links in an energy corridor bypassing Russia that transports around 1 percent of daily world crude oil output west from the Caspian Sea.

Earlier in Kiev, Cheney met Prime Minister Yulia Tymoshenko, whose enthusiasm for NATO has cooled since she signed a letter in January calling for a Membership Action Plan.

Tymoshenko and Yushchenko's coalition collapsed on Wednesday after only nine months, plunging the country into chaos.

EU RESPONSE

European Union president France brokered a ceasefire to the Georgian conflict and EU foreign ministers were meeting in southern France later on Friday to discuss sending civilian monitors to the zone.

EU foreign policy chief Javier Solana said plans were "practically ready" for an EU civilian monitoring mission to Georgia which the bloc hopes will convince Russia to withdraw its forces to pre-conflict lines in Georgia.

The EU, Russia's biggest trading partner, has threatened to suspend talks on a partnership agreement if Moscow fails to withdraw its troops to pre-conflict positions by Sept. 15.

But EU leaders are wary of sanctions which could isolate Moscow, encourage Kremlin hardliners and damage Europe's booming business relationship with Russia.

EU trade chief Peter Mandelson told Reuters in an interview on Friday it was in no-one's interests to use the Georgia crisis to delay Russia's entry into the World Trade Organisation.

The Moscow-led Collective Security Treaty Organisation, known as the ODKB, backed Russia's actions in Georgia on Friday, but stopped short of recognising Georgia's separatist regions as Moscow has done.

In Washington, a U.S. official said Washington would scrap a civilian nuclear deal with Russia intended to lift Cold War restrictions on trade and open up the U.S. nuclear market and Russia's uranium fields to companies from both countries.

"The administration will not be moving forward with the agreement. It will be pulling it back from Congress," said the State Department official, speaking on condition of anonymity.

The United States has used warships to ferry relief supplies to Georgia, in part to send a signal to Moscow. Its biggest ship yet arrived on Friday. The USS Mount Whitney dropped anchor off Georgia's Russian-patrolled port of Poti.

Russia has accused U.S. warships of rearming Tbilisi's defeated army, a charge rejected as "ridiculous" by Washington. (Additional reporting by Conor Sweeney and Oleg Shchedrov in Moscow, Sabina Zawadski in Kiev and Mark John in Avignon; Writing by Jon Boyle and Michael Stott; Editing by Mary Gabriel)

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