* Moscow can back UN statement if no anti-Assad ultimatum
* Statement backed by Russia would be sign of unity
* Russia has vetoed 2 Security Council resolutions on Syria
By Alexei Anishchuk and Steve Gutterman
MOSCOW, March 20 (Reuters) - Russia said on Tuesday it was ready to endorse a U.N. Security Council statement backing U.N.-Arab League envoy Kofi Annan's Syrian peace mission as long it does not present an ultimatum to President Bashar al-Assad's government.
Foreign Minister Sergei Lavrov also repeated Russia's insistence that Syrian government forces and rebels must cease fire simultaneously to end a year of bloodshed, a position that differs starkly to that of the United States.
Lavrov said Russia, which has blocked Security Council action on Syria for months, was prepared to approve a statement or resolution supporting the efforts of U.N.-Arab League envoy Annan. But he added there were "at least two" conditions.
"The Security Council must approve these not as an ultimatum but ... as a basis for the continuation of efforts to reach accord between the Syrian government and all opposition groups," Lavrov said after talks with Lebanon's foreign minister.
A Western-drafted statement supporting Kofi Annan's peace efforts and sending a strong message to Damascus to end violence was circulated on Monday by France. Britain's U.N. envoy said he hoped it would be adopted on Tuesday.
Annan's plan entails a ceasefire, access for humanitarian aid and political dialogue with the Syrian opposition.
Lavrov's remarks suggest that Russia, which has shielded Assad by vetoing two Western-backed Security Council resolutions condemning his government for a year of bloodshed in which over 8,000 people have died, may seek changes to Annan's text.
The draft statement's threat of "further measures" if Syria does not comply within seven days seems unpalatable to Russia.
Moscow does not want Western and Arab nations who seek Assad's removal, saying his military crackdown on a popular uprising has destroyed his legitimacy, to be able to use a U.N. resolution to advance their visions of a solution in Syria.
Assad has given Moscow its strongest foothold in the Middle East, buying billions of dollars worth of Russian arms and hosting a Mediterranean maintenance and supply facility that is Russia's only naval base outside the former Soviet Union.
Adoption of a Security Council statement or resolution with Russian support would raise pressure on Assad and could help Moscow rehabilitate its image after protecting Assad from condemnation with the vetoes in October and February.
China, which joined Russia in both vetoes, may be eager to mend ties with Arab states it relies on for oil supplies.
But Lavrov made clear there were lines Russia would not cross for the sake of unity among global powers. He said Moscow will continue to demand that Assad's government and its opponents cease fire at the same time.
He called for "clear measures to end the violence wherever it comes from - and precisely simultaneously, and not in some order, when it is demanded that the government withdraw all its units from cities and this is not expected of the opposition."
On Monday, the U.S. State Department underscored its insistence that Assad must stop the violence first for any ceasefire to take place. "The sequence that we see is very clear. It is the regime that bears primary responsibility for the violence, and they need to stop first," State Department spokeswoman Victoria Nuland said.
The other condition Lavrov raised for approval of a Security Council statement was that Annan's plan be published.
In his remarks on Tuesday, Lavrov also dismissed earlier media reports that said Russian warships had entered the naval facility at Tartous or were nearby, calling them "fairy tales".
He said only a Russian tanker supporting Moscow's anti-pirate mission in the Gulf of Aden was stationed at the Russian facility at the moment, and that its civilian personnel were protected by a unit of guards.