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The Ukrainian military pushed the rebels out of their best-fortified stronghold in the town of Slaviansk on Saturday (local time), but they have regrouped for a stand in Donetsk, a city of nearly a million people. Rebels also still control strategic buildings in Luhansk near the Russian border.
Separatists said on Tuesday that Igor Strelkov, a Russian military officer from Moscow who until the weekend led rebels in Slaviansk, had assumed command of the "defence of Donetsk".
President Petro Poroshenko has ruled out using air strikes and artillery that might endanger civilians and said on Tuesday night: "There will be no street fighting in Donetsk."
But the government says it has a plan to retake Donetsk and Luhansk and deliver a "nasty surprise" for the rebels.
Military spokesman Andriy Lysenko spelled out the threat on Wednesday, saying: "There's a plan to liberate Ukrainian territory from the terrorists, and it doesn't depend on the readiness or the unreadiness of Strelkov and his underlings to defend, as they call it, the Donbass."
But separatists in charge of a 'mobilisation' centre for the self-proclaimed 'people's republic' said on Wednesday that recruitment of new fighters was continuing at a pace since Strelkov made an appeal for fresh recruits on Tuesday.
About 300 volunteers had come forward to join up since Tuesday, many more than the usual number of 25-30 people per day, separatists at the centre said.
Pro-Russian separatists have been fighting government forces in the Russian-speaking east since April in a conflict in which more than 200 Ukrainian troops have been killed as well as hundreds of civilians and rebels.
The conflict has driven relations between Russia and the ex-Soviet republic to an all-time low and sparked the worst crisis in Russia's relations with the West since the Cold War.
After a patchy performance at the start of the campaign, government forces have been re-invigorated by the Slaviansk victory and signs that rebel calls on Russia for help are now going unheeded.
Poroshenko referred back to those early days of the campaign when, he said, Ukrainian soldiers had refused to carry out orders and refused to fight, a time when "a bunch of provocateurs could stop a brigade of paratroopers or special forces".
"On July 7 the country had 320km of open border (with Russia) ... A month has passed and now the army ensures the border is closed," he said.
German Chancellor Angela Merkel and French President Francois Hollande spoke by phone with Poroshenko on Wednesday, with the aim of restarting talks with separatists on a ceasefire, Merkel's spokesman said.
But hundreds of rebels are setting up barricades and digging in on the outskirts of Donetsk since pouring in from Slaviansk and nearby areas recaptured by the government.
PAYING NEW FIGHTERS
Many of the rebel fighters are from Russia, though Moscow denies supporting their revolt, which began in April after Russia annexed Ukraine's Crimea peninsula following the overthrow of a Moscow-backed president in Kiev.
Despite the rebels' claim of a strong flow of recruits, Strelkov, also known as Igor Girkin, appeared to be disappointed at the number of volunteers coming forward. He told a local rebel TV station that volunteers would be offered monthly pay of 5,000-8,000 hryvnia ($430 to $690) from now on to fight.
"Maybe this will help those people who are hesitating to find the strength in themselves and join the ranks," he said.
But Lysenko derided this as an empty offer: "The terrorists are resorting to all methods to deceive the local population. We are coming across leaflets with promises that they are ready to ... pay 8,000 hryvnia and 20,000 Russian roubles ($600) per month. They are stopping at nothing to try and persuade people to come over to their side."
Many men of fighting age were wary of the call to arms.
In Donetsk, Evhen, a 35-year-old who runs his own business, said: "I personally would only join if the situation became really critical. I never did military service and I have no military experience. I support the idea (of insurgency), but there is no clear support (from Russia). Sensible people worry about how it will all end."
A 19-year-old who would not give his name said: "I won't join them. For a start, I want a united country. Secondly, there are an awful lot of marginals among them. There are robbers. They frighten people and take away their businesses and cars."
APPEAL FOR AID
In Kiev, Prime Minister Arseny Yatseniuk meanwhile appealed to Western institutions and donors for further cash and credit to rebuild infrastructure such as roads, bridges and buildings in the east that have been shattered by the conflict.
But he expressed confidence that Ukraine's compliance with criteria set by the International Monetary Fund meant the Kiev government was on course to secure soon a second tranche of $1.5 billion under a $17 billion IMF programme.
The ex-Soviet republic received a first slice of slightly more than $3 billion in May under a programme drawn up to help it plug holes in its budget and settle a big foreign debt.
But Ukraine told international donors on Tuesday in Brussels that the Fund's bailout was not enough to bring about a full recovery because of the drain caused by the cost of the war against the separatists, and it called on them to join in a "Marshall Plan" to further help Ukraine's recovery.
Ukraine's turn towards the West and away from Moscow has cost it billions of dollars in promised Russian support for an economy on the verge of bankruptcy after years of rule rated by watchdogs as among the world's most corrupt.
Taking up the same theme on Wednesday, Yatseniuk said Ukraine needed further aid to establish functioning infrastructure on the border with Russia.
In addition, Ukraine wanted help to meet an estimated cost of 8 billion hryvnia (about $700 million) to rebuild infrastructure.
Yatseniuk said Ukraine would also want donors' help to work out a "post-rehabilitation" programme to regenerate the Donbass - an economically depressed eastern region of decaying infrastructure in the steel and coal industries - which has become the battleground for the insurgency.
The European Union agreed to add 11 new names to the list of persons targeted with asset freezes and travel bans over the Ukraine crisis and the sanctions are likely to take effect on Saturday, an EU diplomat said.
Ukraine accused Russia of abducting a woman army officer who was captured by separatist fighters in eastern Ukraine.
Nadezhda Savchenko, 33, was seized by pro-Russian rebels in June while she was fighting with pro-government militia on the outskirts of Luhansk on the border with Russia, local media say.
The Ukrainian foreign ministry demanded her release but Moscow said she had been charged with involvement in the deaths of two Russian reporters killed near Luhansk.