The Kremlin ordered major military exercises on Wednesday as concerns about unrest in Ukraine's Crimean peninsula continued to grow and scuffles in the region left one person dead.

The Russian president, Vladimir Putin, ordered an urgent drill of his country's armed forces in western Russia, in what appeared to be a display of sabre-rattling aimed at the new government in Kiev.

The US reacted in a strongly worded message, with the secretary of state, John Kerry, saying that any military intervention in Ukraine would be a "grave mistake".

"For a country that has spoken out so frequently … against foreign intervention in Libya, in Syria, and elsewhere, it would be important for them to heed those warnings as they think about options in the sovereign nation of Ukraine," Kerry said last night.

Putin had earlier instructed his defence minister, Sergei Shoigu, to place Russia's military in a state of high alert for drills in the western military district, bordering Ukraine. The defence ministry denied the drills had anything to do with the political situation in Kiev, where the government of President Viktor Yanukovych was in effect toppled at the weekend.

But the move comes amid increasingly forthright statements from Moscow that the rights of ethnic Russians in Ukraine are being infringed.

Shoigu told a defence ministry meeting that forces must "be ready to bomb unfamiliar testing grounds" as part of the drill.

In his blunt message Kerry also announced the Obama administration was planning $1bn in loan guarantees and additional funding for Ukraine. But he said that US policy towards Ukraine was not aimed at reducing Russia's influence. "This is not Rocky IV," Kerry said. "It is not a zero-sum game. We do not view it through the lens of East-West, Russia-US or anything else. We view it as an example of people within a sovereign nation who are expressing their desire to choose their future. And that's a very powerful force."

Crimea has a largely pro-Russian population and earlier this week Ukraine's acting president, Oleksandr Turchynov, warned there was a "serious risk" of separatism in the region.

In the regional capital of Simferopol on Wednesday there was a gathering of around 10,000 Crimean Tatars, a Muslim ethnic group that supports the peninsula remaining part of Ukraine. Waving Ukrainian flags they chanted: "Ukraine is not Russia."

The group clashed with a smaller pro-Russian rally nearby in which participants waved Russian flags. Protesters shouted abuse at each other, with the atmosphere growing more hostile by afternoon. The pro-Russian group swelled to about 5,000 later on as more protesters arrived on buses from the port city of Sevastopol, where the Russian Black Sea fleet is based.

A smattering of rocks flew as the two sides engaged in fistfights at the frontline. The anger in the faces of both sides was visible shortly before the violence as they catcalled and jeered at one another and beckoned at each other offering the occasional middle-finger salute.

"You're defending all the millionaires who have stolen the land," shouted one angry Tatar. The Russians responded with a taunting rally cry of "Berkut, Berkut, Berkut", a reference to the police special unit responsible for much of the violence against protesters in Kiev last week that left at least 82 dead.

"Allahu Akbar!" chanted the Tatars as the other side responded with a rally cry of "Russia, Russia, Russia". Those in the Tatar camp held signs reading: "Ukraine to Europe." "We just want to be free," said Arsen Bilyalov a 36-year-old Tatar.

The clashes resulted in several serious injuries on the Russian side, as well as one death, apparently from a heart attack. The parliamentary session was cancelled as a result of the violence outside.

Ukraine's acting interior minister said he was doing all he could so as not to inflame tensions in Crimea further. "The police and all enforcement bodies in Crimea received instruction from me – at any cost do not provoke any conflict, any military confrontation with the civilians," Arsen Avakov said.

"I'm demanding law enforcement officers from Sevastopol to Simferopol to do all possible to prevent clashes between radical pro-Russian forces with any other radicals, including those who stand for European integration or Crimean Tatars," he added.

Avakov also announced on Wednesday that the notorious Berkut riot police, elite troops responsible for much of the violence over the past three months, had been disbanded.

"This special unit has totally discredited itself," he said, adding that a new unit would be established in time. The 4,000 former Berkut troops will now have to pass a revalidation exam in the next 15 days to determine whether they will serve in the new structure. He added that some top-ranking Berkut officers had fled already, and police were searching for them.

However, in another sign that Crimea is the only part of Ukraine where the new authorities are not welcome, a number of Berkut units returning to the region from Kiev have received a hero's welcome this week, and on Wednesday the newly-appointed pro-Russia mayor of Sevastopol invited the elite squad to join local law enforcement.

Since Yanukovych fled the capital at the weekend the protest movement has moved to take over the mantle of government, attempting to build bridges with the police and intelligence services, and continuing to patrol the capital with its own "self-defence units".

Turchynov, has drawn up a cabinet, which he announced to the crowds on Independence Square on Wednesday evening. It included a number of key figures in the protest movement, including the journalist Tetiana Chornovol, who was severely beaten after investigating government corruption and will now head an anti-corruption bureau.

Presidential elections have been set for 25 May. Frontrunners include the former boxer Vitali Klitschko and Yulia Tymoshenko, the former prime minister who was released from jail on Saturday.

She has not yet said whether she will run. Tymoshenko's ally Arseny Yatsenyuk was named as acting prime minister by Turchynov, to a mixed reception from the crowd.

Ukrainian pPolice are still searching for Yanukovych, who has been the subject of various rumours since he fled. The interim authorities said they believed he was hiding in Crimea, after a failed attempt to leave the country in a private jet from Donetsk airport. There were unconfirmed reports in Ukrainian media that Yanukovych had left Crimea by sea and was now in Russia with his two sons. One Russian news outlet claimed Yanukovych had been spotted at a government sanitorium just outside Moscow.

However, a top Russian foreign policy official told Russian media on Wednesday evening he was "absolutely certain" that Yanukovych was not in Russia. Mikhail Margelov added that he thought it unlikely that Russia would offer asylum to the disgraced leader, although just a day earlier a top Russian MP had said Moscow still considered Yanukovych to be the legitimate president of Ukraine.

Avakov said Ukraine's new authorities had pulled back from the search for Yanukovych in Crimea, fearing that treading too heavily could destabilise the fragile situation further.

"We decided the fate of Crimea is more important," he said.