(Adds Putin quotes paragraphs 6-9)
* Rouble devalued again, expected to weaken further
* Medvedev calls for government unity during crisis
* Number of registered jobless seen up 69 pct in 2009
* Rouble at new all-time low versus euro
By Gleb Bryanski and Toni Vorobyova
MOSCOW, Dec 29 (Reuters) - Russia devalued the rouble again on Monday and Kremlin leaders urged government unity to deal with the biggest economic challenge in a decade.
Russia's central bank began a gradual depreciation of the rouble in November in response to slumping oil prices, a worsening economy and investors' flight from emerging markets.
Prime Minister Vladimir Putin, facing his first economic crisis, has ruled out any sharp rouble moves. Russians are mindful of the 1998 currency collapse. Unemployment is on the rise and real disposable income is falling.
"We can have different points of view on various problems. But at a time of global challenges it is important to maintain the unity of the government," President Dmitry Medvedev told a cabinet meeting.
Russia's rouble policy is a topic of debate. Some economists say a gradual devaluation, designed to provide a softer landing than a big, one-off cut, is actually backfiring by pushing the economy faster into recession.
Putin said the exchange rate policy was guided primarily by ordinary Russians' interests.
"Unlike during the past crises we do not shoot from the hip ... like they are forced to do now in some other countries. We consciously use our reserves to enable an ordinary person to calmly take his own decision," Putin said.
BE OBJECTIVE, PUTIN TELLS REPORTERS
Putin also told journalists not to fan public concern about the country's sharp economic downturn.
"I ask you to report the unfolding events objectively, do not rachet up fears or hysteria -- there are no grounds for them," Putin told reporters in the government press centre after the cabinet meeting.
The rouble weakened to 35.08 to a euro-dollar basket in the first minutes of trade on Monday before stabilising around 34.80, according to Reuters data, down around 1.5 percent or 50 kopecks from its close on Friday.
The previous support level was about 34.30.
After Monday's fall -- the ninth time the central bank allowed the rouble to weaken this month -- the rouble/dollar rate hit its weakest level since 2004 while the rouble hit a new all-time low against the euro.
The currency is now down 17 percent against the basket this year and 18.6 percent below historic peaks in August. Since then the price of oil, the main export, has fallen over 70 percent.
"With such a backdrop, which has turned sharply negative ... we will most likely get another 10 percent (rouble devaluation) in January," said Anton Tabakh at Troika Dialog, saying the Russian economy faced an array of problems.
"The coffin on wheels has found its way into our street and is looking for a way into our house," he said.
Unlike a decade ago, when Russia had little choice but to allow a currency collapse, this time it has the world's third biggest reserves. It has used over $100 billion of the now-$450 billion cash pile to help smooth out exchange rate moves.
NO SHARP CURRENCY MOVES
The central bank says it will not alter its policy and allow a sharp one-off move. On Monday, it extended into next year its foreign currency asset limitations on commercial banks, in a bid to deter speculators.
Calls from Medvedev and Putin for team spirit came after the first signs of disagreement among officials on emergency measures and amid signs of public disquiet.
So far there have been no major protests in Moscow over the financial crisis, and state-controlled television channels have devoted little air time to rouble devaluations.
But officials say rising unemployment and a fall in real disposable income could lead to greater unrest.
Health and Social Development Minister Tatyana Golikova said on Monday the number of Russians officially registered as unemployed could reach 2.1 to 2.2 million people next year.
That represents a 69 percent increase from the 1.30 million officially registered as unemployed in November. The actual jobless figure, including those not claiming benefits, was 5.0 million in November, the state statistics agency reported.
At the same time, the economy is expected to have contracted this month. Putin estimated full-year GDP growth will stand at 6.0 percent, down from the 6.5 percent expansion reported in the first 11 months.
Some analysts still reckon that despite possible social unease, a free-floating exchange rate is the only way forward.
"Of course there will be panic, but there is no painless way out of the current situation," said Maxim Oreshkin at Rosbank.
"The question is what is ultimately worse for the population: the loss of some value of their savings, or the ongoing devaluation expectations which lead to high (interbank interest rates), resulting in job cuts?" (Additional reporting by Yelena Fabrichnaya and Gleb Bryanski; writing by Dmitry Zhdannikov, editing by Tim Pearce)