At the headquarters of the Vostok Battalion on the outskirts of Donetsk, the rebel in command was ordering an attack on 30 Ukrainian soldiers and two fighting vehicles in a nearby town. "Shoot to kill," he said, speaking with a subordinate over one of three mobile phones he carries. "What negotiations? If they wave a white flag, then of course that's different."

The commander, a Russian army veteran – who like all the men in the battalion is known only by a nickname ("Major") – told his deputies to assemble 40 men and tank-busting weapons. A few minutes later, a soldier ran in with six rocket-propelled grenade launchers. Throughout the day, fighting vehicles and lorries loaded with armed men roared in and out of the base.

As the possibility recedes of a "Crimean scenario" – Russian troops intervening in eastern Ukraine – the pro-Moscow Vostok Battalion has emerged as the leading force in the fight against Kiev's attempts to retake control of the east. Along with the Army of the Southeast in Luhansk and a militia in Slavyansk led by Russian citizen and alleged intelligence agent Igor Girkin, better known by his nom de guerre "Strelkov," iIt is Vostok that will define the course of the mostly low-level war with Kiev forces.

The militia has about 500 men, according to its leader, Alexander Khodakovsky, who was regional head of the elite Alfa special forces unit under former president Viktor Yanukovych, and handfuls of new recruits have been joining each day. Since it was formed in April, some analysts have worried that Vostok is an incipient private army directed by – or at least linked to – Russian intelligence. But locals welcomed the fighters with cheers when they fired into the air at an anti-Kiev rally during the recent presidential election.

Khodakovsky and his commanders are vague about their goals, saying their immediate task is to drive pro-Kiev forces from their region. But they are vehemently opposed to the new pro-western government brought to power following the Euromaidan protests in Kiev this winter – during which Khodakovsky and his special forces unit participated in violent clashes with the demonstrators.

"To side with America now, at a time when the world is getting extremely polarised, means to go against Russia. But how can the south-east be against Russia? We are trying to prevent us from becoming an enemy of Russia," Khodakovsky told reporters as his men showed off a variety of weaponry at the Donetsk Botanical Garden on Sunday.

So far, government forces have been unwilling or unable to take heavily populated rebel strongholds, but pro-Russian forces have also failed to achieve decisive victories. Ukraine's prosecutor general said this week that, excluding rebel forces, 181 people have died, including 59 soldiers, and 293 have been wounded since fighting started in April.

On Friday, Vladimir Putin briefly met Ukrainian president-elect Petro Poroshenko at the D-day commemorations in France. A Kremlin spokesman said the two leaders urged a "speedy end to the bloodshed in south-eastern Ukraine as well as to fighting on both sides". "It was confirmed that there is no other alternative to resolve the situation than through peaceful political means," the spokesman said.

On Thursday, President Obama gave Russia a one-month deadline to stop the flow of fighters and weapons into Ukraine after a string of clashes at the border, which is now at least partially under rebel control.

Fighting continued on Friday around a border post at Marynovka, where 16 rebels were killed after overnight air strikes, Kiev said. The major border crossing at Dovzhansk and another at Krasnopartizansk are reportedly under rebel control. The government has ordered the closure of the border in Luhansk and part of Donetsk regions but rebels say they control 150-200km of the frontier.

The Vostok Battalion does include Russian fighters, and the bodies of 31 members were sent back to Russia last week after a battle at Donetsk airport. But more than a dozen interviews over several visits by the Guardian suggested Vostok is largely comprised of Ukrainian volunteers with nicknames like "Forest Lord," "Psycho," "Wild Man" and "Beaver". Although its sources of funding and weapons are not entirely clear, it does not seem to enjoy large-scale Russian military support, with kit that ranges from sophisticated surface-to-air missiles to battered hunting rifles.

On a recent afternoon, members of the battalion's mechanical section were welding an anti-aircraft gun to the back of a lorry to create a vehicle straight out of Mad Max. "If we had Russian military hardware, you would see it," said "Mamai," a garrulous Vostok member from Russia's republic of North Ossetia. Vostok commanders said they had taken their weapons mostly from captured Ukrainian military facilities.

Some members of the battalion look like professional soldiers, but Mamai said he doesn't receive money to fight. Another Russian member named "Varan" ("Monitor Lizard") said he received $100 (£70) a week for living expenses but maintained that the men were volunteers, not mercenaries on Moscow's payroll. Yet Russian authorities have at least tacitly encouraged volunteers to go to Ukraine. Varan said a military enlistment office tipped him off about a group of fighters forming in Rostov-on-Don who then walked through a border crossing as civilians, receiving arms in Donetsk.

The Vostok Battalion has taken part in most of the heaviest fighting in eastern Ukraine in recent weeks, including a checkpoint battle near Karlovka, the bloody attempt to seize the Donetsk airport and the continuing struggle to break the Ukrainian encirclement of Slavyansk. The unit truly asserted its dominance last week, however, when – after a tense standoff – Vostok fighters kicked other rebel groups out of the regional administration building, which was occupied by the self-declared Donetsk People's Republic in April. A Vostok commander said they were there primarily to bring looters to justice, and the unit has since assumed a quasi-law-enforcement function in place of the impotent police.

Alexander Sheremyet, a protester who was involved in the administration building occupation from the first days, said Vostok is now the most powerful force defending the Donetsk People's Republic, but denied they were controlling the fledgling government.

"They gathered experienced veterans, they have the most strength, but their tasks are only military," he said.

The battalion's Russian members include men who served in previous wars on its borderlands. Speculation began to swirl that the unit is connected to Russian intelligence after fighters from Chechnya were found to be fighting with it. Its name – which means "East" – suggests a Chechen unit run by Russia's military intelligence agency, which was active during the 2008 Russia-Georgia war.

Mark Galeotti, a New York University professor who studies the Russian security services, argued that the two are probably linked and said the emergence of the Vostok Battalion could represent the Kremlin tightening its control on the situation in eastern Ukraine.

"Moscow needs an instrument," Galeotti said. "But also insofar that they're going to try to assert their authority through the Donetsk People's Republic hierarchy, they need to make sure those guys have credible force at their disposable, not just a collection of thugs."

Chechen fighters in Donetsk, one of whom said he served in the original Vostok Battalion, denied that the current Vostok had any connection with the disbanded Chechen unit. Other members said its name merely reflected its fight in eastern Ukraine.

Pavel Felgenhauer, a Moscow-based defence analyst, raised questions about the unit's source of funding. "Someone's paying them; war without money doesn't happen," he said. "Most likely there's a lot of criminals involved doing different kinds of rackets, but that's not a means for an operation of such magnitude to buy weapons, pay bribes to get weapons in, for ammo."

While it is unlikely Vostok is being financed directly by the Kremlin, it could be supported by pro-Kremlin businessmen, as other separatists have been. Konstantin Malofeyev, an oligarch known for his support for Russian expansionism, reportedly financed Russian citizens promoting separatism in Crimea including Strelkov and Alexander Borodai, the recently declared prime minister of the Donetsk People's Republic. Strelkov and Borodai have said they are friends and were both previously employed by Malofeyev in Moscow.

Borodai denied receiving funding from the Russian government and told the Guardian he didn't know if the people's republic had taken donations from Malofeyev or other Russian oligarchs.

Khodakovsky's connections and allegiances are unclear. According to Konstantin Mashovets, a Kiev-based defence analyst, he would have been appointed Alfa head by either Yanukovych or his security service chief. The former president was known to be closely allied with Rinat Akhmetov, the most powerful oligarch in eastern Ukraine, who has seemed to waver between Kiev and the east during the current uprising.

Khodakovsky has denied receiving financial backing from Akhmetov or having connections with the Kremlin, and Vostok commanders said they don't know of any rich sponsors.

Dmitry Durnev, a Donetsk journalist, said local rebel leaders have yet to form permanent alliances and are probably "taking money from everyone".

Meanwhile, the unit continues to grow in numbers and influence. One commander nicknamed "Lithuania," a coal miner who joined late last month, said he enlisted because Vostok was the rebel unit with the most discipline and "spirit and ability" to fight the "Kiev junta".

"The Vostok Battalion is actually engaging in military operations against this scum; it doesn't just sit in its base," he said. "We're hoping for Russian assistance, so our brothers will come to help us.