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 wellbeing and security," Cheney said after meeting President Viktor Yushchenko, a pro-Western 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 when Soviet ruler Josef Stalin attempted to force peasants into collective farms.
Cheney, Yushchenko and their wives each placed a bowl of grain and flowers with a candle in the middle in front of the memorial, then bowed their heads in silence.
Cheney`s visit was likely to anger further 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 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 over 7 percent on Friday to their lowest level in more than two years and the Central Bank intervened on Thursday to prop up the rouble.
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 Kyiv 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 by the Ukrainian nation 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 one percent of daily world crude oil output west from the Caspian Sea.
Earlier in Kyiv, 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 has quarrelled with Yushchenko frequently and their coalition collapsed on Wednesday after only nine months, plunging the country into chaos.
European Union president France brokered a ceasefire to the conflict and EU foreign ministers were meeting in southern France later on Friday to discuss sending civilian monitors to the zone.
A decision to deploy an initial 200-plus force could be taken in just over a week, after French President Nicolas Sarkozy returns from a trip to Moscow, an EU official said.
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 in Georgia 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.
A U.S. official said Washington was likely to 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 United States has used warships to ferry relief supplies to Georgia as a way of showing support for its ally and sending a signal to Moscow and its biggest ship yet arrived on Friday.
The USS Mount Whitney, a sophisticated command warship which acts as the flagship of the U.S. Sixth Fleet, dropped anchor off Georgia`s Russian-patrolled port of Poti on Friday.
Russia has accused U.S. warships ferrying aid to Georgia of rearming Tbilisi`s defeated army, a charge rejected as "ridiculous" by Washington but which highlights Moscow`s suspicions over the increasing number of NATO warships in the Black Sea, traditionally dominated by its navy.
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