* Several days of fighting in east
* Rebels hold out in Slaviansk
* Violence in Odessa spreads unrest across south
* Western countries focus on May 25 presidential election
* Rebels aim to hold referendum on secession on Sunday
Tuesday was generally quieter than past days in most of eastern and southern Ukraine, but violence flared in the eastern port of Mariupol in the evening, according to local media.
The Web site 0629.com.ua posted pictures of tyres blazing outside the city council building, which had already been occupied by pro-Russian protesters and thick smoke pouring over the city centre. Some streets were barricaded by buses or walls of tyres and people heard shooting near a local military base.
In Kramatorsk, a separatist-held town in the east that saw an advance by Ukrainian troops at the weekend, the coffin of 21-year-old nurse Yulia Izotova was carried through streets stilled by barricades of tyres and tree trunks on Monday. Scattered red carnations traced the route.
At the Holy Trinity Church, seven priests led mourners in prayer for a woman killed by large calibre bullets, which the townsfolk believe were fired by Ukrainian troops.
"They shoot at us. Why? Because we don't want to live with fascists?" asked 58-year-old passport photographer Sergei Fominsky, standing with his wife among the mourners. "We're not slaves. We kneel to no one."
In Odessa, a previously peaceful, multi-ethnic Black Sea port where more than 40 people were killed on Friday in the worst day of violence since a February revolt toppled Ukraine's pro-Russian president, pall-bearers carried Andrey Biryukov's open casket from a van to the street corner where he was shot.
A pro-Ukrainian activist, Biryukov, 35, was killed during a day that began with hundreds of pro-Russian sympathisers armed with axes, chains and guns attacking a Ukrainian march, and ended later that night with the pro-Russians barricaded inside a building that was set on fire, killing dozens.
A small crowd of about 50 people stood around the body, covering it with carnations and roses. A Ukrainian flag fluttered in the wind, and a patriotic song about dead heroes was played from a sound system.
Relatives wept and a young woman fell on her knees crying loudly. The corner where the man died was decorated with flowers and small Ukrainian flags.
"The government has failed to protect its own people. The police have failed miserably," said Nikita, a grizzled 56-year-old with a Ukrainian yellow and blue arm-band.
Sergei, in his 40s, who also came to mourn, said violence "was imported to Odessa".
"We were proud of Odessa as a unique place where people used to live in peace, regardless of their beliefs and religion and race," he said. "Now this is all gone."
The surge in violence has changed the tone of international diplomacy, with even cautious European states speaking increasingly of the likelihood of war in a country of around 45 million people the size of France.
"The bloody pictures from Odessa have shown us that we are just a few steps away from a military confrontation," German Foreign Minister Frank-Walter Steinmeier said in interviews published in four European newspapers.
The next few days could prove decisive: separatists in the eastern Donbass region say they will hold a referendum on secession on Sunday May 11, similar to the one that preceded Russia's annexation of Crimea.
The U.S. State Department denounced any attempt at a vote as "bogus" and promised more sanctions if Russia used it, as in Crimea, to send in forces or annex more territory: "This is the Crimea playbook all over again," a spokeswoman said.
Secretary of State John Kerry said he would meet ministers in Europe next week to discuss the next steps on Ukraine.
Two days before the vote, Friday May 9, is the annual Victory Day holiday celebrating the Soviet Union's victory over Nazi Germany. Moscow has been openly comparing the government in Kiev to the Nazis, and Ukrainian officials say they are worried that the day could provoke violence. In Moscow, there will be a massive parade of military hardware through Red Square, a Soviet-era tradition revived by President Vladimir Putin.
The past few days have seen government forces press on with an offensive but make little progress in the east, where separatist rebels have so far held firm at their main outpost in the town of Slaviansk and shot down three Ukrainian helicopters.
Interior Minister Arsen Avakov said on Tuesday more than 30 separatists had been killed in fighting around Slaviansk, but there was no confirmation of such a figure. The rebels, who triggered fighting in the area on Monday by ambushing government troops, said four of their number had been killed.
At roadblocks in the town, some armed fighters have been replaced by civilians, like Alexandra, in her late 20s, who said she leaves her 10-year-old daughter at home each morning, puts a starting pistol in her belt and walks to the barricades. The tactic of putting civilians at the front could make a government offensive more difficult.
"We have two options - to use heavy artillery ... wipe everything out, put the flag up and report that everything has been done. The second option is a gradual blockade, destroying provocateurs and sabotage to prevent injuries among the population. We are carrying out the second scenario," said acting defence minister Mykhailo Koval, explaining why the operation has taken so long and achieved so little.
Since a pro-European government took power after the uprising that toppled pro-Russian President Viktor Yanukovich, Putin overturned diplomatic convention by declaring Moscow's right to send troops across borders to protect Russian speakers.
In March, Russia seized and annexed Crimea, and in the weeks that followed, armed separatists have taken control of most of the eastern Donbass coal and steel region, which accounts for around 15 percent of Ukraine's population and a third of industrial output.
Moscow has tens of thousands of troops massed on Ukraine's eastern frontier. The outbreak of violence in Odessa, hundreds of kilometres away near a Russian-occupied breakaway region of neighbouring Moldova, means the unrest has spread across the breadth of southern and eastern Ukraine.
Western countries say Russian agents are directing the uprising and Moscow is stoking the violence with a campaign of propaganda, broadcast into Ukraine on Russian state channels, that depicts the government in Kiev as "fascists".
"Russia sometimes sounds as if it's refighting WW2. Fascism all over the place. Enemies everywhere. Ghosts of history mobilised," tweeted Swedish Foreign Minister Carl Bildt.
However, so far Western concern has not been matched by any serious action that might dissuade Putin. The United States and the European Union have imposed limited sanctions on lists of individual Russians and small firms, but have held back from measures designed to hurt Russia's economy broadly.
Nonetheless, a senior finance ministry official in Moscow said Russian GDP could shrink again this quarter.
NATO has made clear it will not fight to protect Ukraine, instead beefing up defences of its nearby member states. NATO's top military commander, U.S. Air Force General Philip Breedlove, said on Monday Russia had used special forces in eastern Ukraine and he now believed Moscow might be able to achieve its goals without resorting to a conventional invasion.
Western leaders have threatened to impose tougher sanctions on Russia if it interferes with presidential elections in Ukraine set for May 25, and most of their diplomacy has been centred around that date.
"If (the election) doesn't take place, there will be chaos and the risk of civil war," French President Francois Hollande said. "The Russians, Vladimir Putin, at the moment want this election not to happen so as to maintain the pressure. It's up to us to convince them."
Petro Poroshenko, a Ukrainian confectionery baron who is front-runner in the presidential election, said the vote would go ahead despite the unrest: "We hope that we will be able to complete the anti-terrorist operation before the election. And where we cannot do so - we will surround (those places) and not allow them to interfere with the election."
But Moscow has increasingly dismissed the prospect, suggesting it will not accept the winner of the vote any more than it accepts the interim government in power since February.
"Holding elections at a time when the army is deployed against part of the population is quite unusual," Russian Foreign Minister Sergei Lavrov told a news conference.