Ukraine's president has said that there was a "real danger" Moscow would seize further territory after the referendum in Crimea, and he accused "Kremlin agents" of orchestrating turmoil in the Russian-speaking east of his country.

Acting leader Oleksander Turchinov said there was every possibility that Russia would advance deeper into Ukraine following Sunday's poll, which has been condemned by the west as illegal. He told parliament: "The situation is very dangerous. I'm not exaggerating. There is a real danger from threats of invasion of Ukrainian territory. We will reconvene on Monday at 10am."

A group of Russian commandos advanced beyond Kremlin-occupied Crimea on Saturday and landed by helicopter in an area of southern Ukraine under Kiev's control, Ukraine's defence ministry said. Some 60 Russian troops arrived at 1.30pm in the village of Strilkove, in Kherson province, 5km beyond the autonomous Crimean border. They came in four helicopters. Another 60 flew in in six helicopters at 3.30pm.

Early reports suggested that Ukrainian forces evicted them, but the Russian contingent still appeared to be there on Saturday night. A spokesman for Ukraine's border guard service, Oleg Slobodyan, said the Russian soldiers had taken up positions next to a gas production facility, backed by three armoured personnel carriers. Ukrainian troops had reportedly retreated to a nearby crossroads.

Ukraine's foreign ministry dubbed the incursion a "military invasion by Russia". It demanded that Moscow withdraw its forces and said Ukraine "reserves the right to use all necessary measures" to stop the invasion. The area, Arbatskaya Strelka, is a long section of land running parallel to Crimea. Since independence it has been in Kherson province, but the land was originally part of Soviet Crimea and Vladimir Putin may be attempting to restore this Communist-era border.

Most of the infrastructure that supplies Crimea with water and electricity is in the Kherson region. Reports suggest that Crimea's secessionist authorities have claimed the gas production company that owns the facility, which would explain the arrival of Russian troops.

Ukraine's acting foreign minister, Andriy Deshchyta, told the Observer on Saturday that it is essential that the new government in Kiev, supported by the EU and the US, resists what he called Russian "provocations". He said he was prepared to discuss greater autonomy for Crimea – but only with the proper "legal authorities" there, and not while there were "guns on the streets". He described the referendum as "totally illegal". In Kiev the Rada, Ukraine's parliament, voted to dissolve the regional assembly in Crimea that organised Sunday's poll and has already endorsed union with Russia.

At the UN security council in New York, Russia vetoed a US-backed motion declaring the Crimea referendum invalid. The Russian envoy, Vitaly Churkin, claimed that Crimea was given illegally to Ukraine in Soviet times – a view apparently held by Putin. Russia's vote was the only no, with China abstaining, while 13 nations voted yes. The US ambassador to the UN, Samantha Power, said the result underscored Moscow's profound isolation over Crimea. Russia could not, she said, "deny the truth that there is overwhelming international opposition to its actions".

The mood in the east, meanwhile, remains febrile following three deaths in two days in the cities of Donetsk and Kharkiv. On Thursday evening, Russia's foreign ministry posted an ominous statement saying that Moscow reserved the right to "protect" ethnic Russians in Ukraine. A day later, following talks with US secretary of state John Kerry in London, Russia's foreign minister, Sergey Lavrov, said no invasion was "planned".

There was more violence on Saturday when pro-Russian protesters stormed Donetsk's security service. Both cities have seen large pro-Russian demonstrations stirred up – Kiev says – by Moscow and its operatives on the ground.

Addressing parliament, and speaking to the political faction of fugitive president Viktor Yanukovych, who fled to Russia, Turchinov declared: "You know as well as we do who is organising mass protests in eastern Ukraine. It is Kremlin agents who are organising and funding them, who are causing people to be murdered."

On Saturday, a local journalist in Kharkiv, Zurab Alazania, told the Observer that "Russian tourists" from across the border were travelling throughout the region – with a hardcore of about 1,000 pro-Russian activists inflaming tensions. "The mood is dangerous. It's difficult to live here. There are a lot of thugs in the city." He warned: "There can be further bloodshed, not only in Kharkiv."

Two men, aged 21 and 30, were killed by buckshot late on Friday when pro-Russian demonstrators besieged an office of the far-right Ukrainian nationalist group Right Sector, which rose to prominence fighting riot police in Kiev over the winter. Police said 32 Right Sector activists and six pro-Russian demonstrators were detained and a number of weapons seized.

A spokesman for Right Sector in Kharkiv said his group had been besieged in their office overnight by pro-Russian activists firing shotguns and rifles and throwing petrol bombs and stun grenades.Kharkiv governor Ihor Baluta, newly appointed by the interim authorities in Kiev, said the "well-planned provocation by pro-Russian activists" began when unidentified men in a minibus provoked a confrontation with pro-Russia demonstrators and then drove off. When pursuing demonstrators caught up with the vehicle, it was parked outside the nationalists' building.

The Right Sector spokesman, quoted by Interfax-Ukraine news agency, said his group had taken no part in the initial clash and believed the minibus was left outside its office by others.

The prominence of groups like Right Sector in positions of influence in Kiev, and measures such as a short-lived move last month to end the use of Russian as an official language, have led Russia to accuse leaders of a "coup" in Ukraine of planning to impose "fascism" and discriminate against Russian speakers.

In Moscow, a senior foreign ministry official with responsibility for human rights issues, Konstantin Dolgov, said on Twitter that the arrest in Kharkiv of people he described as "neo-fascist militants" must be followed by wider action to "neutralise and punish rampant extremists".

Western powers, preparing economic sanctions against Russia over Crimea, largely dismiss Russia's characterisation of the new authorities in Kiev as the successors of Nazi-allied Ukrainian forces that fought the Red Army in the second world war.