(Adds Putin comments)
* Putin's move could ease East-West tension over Ukraine
* Russian markets rise, euro and dollar strengthen
* No major new troop movements in Ukraine's Crimea
* U.S. suspends military engagements, trade talks with Russia
MOSCOW/KERCH, Ukraine, March 4 (Reuters) - President Vladimir Putin said on Tuesday that Russia saw no need to use military force in the Crimea region of Ukraine for now, in remarks apparently intended to ease East-West tension over fears of war in the former Soviet republic.
The use of force by Russia in Ukraine would be a choice of last resort, Putin said, and sanctions being considered against Moscow by the West would be counter-productive.
Putin told a news conference at his state residence outside Moscow there had been an "unconstitutional coup" in Ukraine and ousted leader Viktor Yanukovich, an ally of Russia, was still the legitimate leader of the country despite giving up all power.
Earlier on Tuesday, Putin ordered troops involved in a military exercise in western Russia, close to the border with Ukraine, back to their bases.
Russian financial markets rebounded after sharp falls on Monday, and the euro and dollar rose in Japan, though Moscow's forces remained in control of Ukraine's Crimea region, seized bloodlessly after Yanukovich was ousted last month.
Russia paid a heavy financial price on Monday for its military intervention in Ukraine, with stocks, bonds and the rouble plunging as Putin's forces tightened their grip in Crimea, whose population is mainly ethnic Russian.
The Moscow stock market fell more than 10 percent on Monday, wiping nearly $60 billion off the value of Russian firms, but Russian stock indexes rose more than 4 percent early on Tuesday before slipping back again slightly, though still up on the day.
Putin said the turmoil in Russian markets was a "tactical, temporary" decision by investors.
U.S. Secretary of State John Kerry will propose ways for a negotiation between Russia and Ukraine to be overseen by a multilateral organisation when he visits Kiev on Tuesday.
NATO allies will hold emergency talks on the crisis on Tuesday, for the second time in three days.
In further pressure on Kiev, Russia's top gas producer Gazprom said it would remove a discount on gas prices for Ukraine from April, Interfax news agency cited the company's chief as saying on Tuesday. 1/8OD:nL6N0M11Q5 3/8
However, Gazprom chief Alexei Miller also said the company could offer Ukraine a loan of $2-3 billion to pay off the country's debt of more than $1.5 billion after Ukraine said it was unable to pay in full for gas deliveries in February, Interfax news agency said.
Putin said at the weekend that he had the right to invade Ukraine to protect Russian interests and citizens after Yanukovich's downfall following months of popular unrest. Russia's Black Sea Fleet has a base in Crimea.
But the military exercises in central and western Russia, which began last week and raised fears that Russia might send forces to Russian-speaking regions of east Ukraine, were completed on schedule.
"The supreme commander of the armed forces of the Russian Federation, Vladimir Putin, gave the order for the troops and units, taking part in the military exercises, to return to their bases," Kremlin spokesman Dmitry Peskov was quoted as saying by Russian news agencies.
Although the end of the exercises had been planned, the announcement sent a more conciliatory message than much of the rhetoric from Russian officials, who say Moscow must defend national interests and those of compatriots in Ukraine.
Putin is dismayed that the new leadership in Ukraine, the cradle of Russian civilisation, has plotted a course towards the European Union and away from what had been Moscow's sphere of influence during generations of Soviet Communist rule.
Moscow's U.N. envoy told a stormy meeting of the Security Council that Yanukovich had sent a letter to Putin requesting he use Russia's military to restore law and order in Ukraine.
Ukraine said observers from the Organization for Security and Cooperation in Europe, a pan-European security body, would travel at its invitation to Crimea in an attempt to defuse the military standoff there.
The United States has begun spelling out its response to Russia's incursion, announcing a suspension of all military engagements with Russia, including military exercises and port visits, and freezing trade and investment talks with Moscow.
President Barack Obama met national security advisers on Monday to discuss how the United States and its allies could "further isolate" Russia, a White House official said.
"Over time this will be a costly proposition for Russia," Obama told reporters.
The State Department said the United States was preparing to impose sanctions on Russia, although no decisions had yet been made.
Members of the U.S. Congress are looking at options including sanctions on Russia's banks and freezing assets of Russian public institutions and private investors, but they said they wanted European states to step up their involvement.
A Kremlin aide said that if the United States did impose sanctions, Moscow might drop the dollar as a reserve currency and refuse to repay loans to U.S. banks.
An International Monetary Fund mission is in Kiev to discuss financial assistance for Ukraine to help it avoid bankruptcy. Kiev's new leaders want a financial package worth at least $15 billion, with a quick release of some of the cash.
The European Union has threatened unspecified "targeted measures" unless Russia returns its forces to their bases and opens talks with Ukraine's new government.
Western leaders have sent a barrage of warnings to Putin against armed action, threatening economic and diplomatic consequences, but are not considering a military response.
There was no immediate sign of any new movements by Russian forces in Crimea overnight although Ukraine's acting president said on Monday that Russia's military presence on the Black Sea peninsula was growing.
Ukrainian officials said Russia was building up armour on its side of the 4.5-km (2.7-mile) wide Kerch strait between the Crimean peninsula and southern Russia.
Russian forces shipped three truckloads of troops by ferry into Crimea after taking control of the border post on the Ukrainian side, Ukraine's border guards spokesman said.
Vladimir, a 50-year-old cab driver, said people do not want the Russians to leave.
"When they are here, it is safer," he said, voicing the opinions of some in the region who fear a return to the chaos in Ukraine after the collapse of the Soviet Union.
Kiev's U.N. ambassador, Yuriy Sergeyev, said Russia had deployed roughly 16,000 troops to Crimea since last week.
Both sides have avoided bloodshed, but the market turmoil on Monday highlighted damage the crisis could wreak on Russia's vulnerable economy, making it harder to balance the budget and potentially undermining business and public support for Putin.
EU foreign ministers held out the threat of sanctions if Moscow fails to withdraw its troops from Ukraine, while offering to mediate, alongside other international bodies.
EU leaders will hold an emergency summit on Thursday.
(Additional reporting by Pavel Polityuk and Natalia Zinets in Kiev, Andrew Osborn in Sevastopol, Thomas Peter in Kerch, Mike Shields in Vienna; Writing by Timothy Heritage and Giles Elgood)