Pro-Russian separatists occupying the regional government building in Ukraine's eastern city of Donetsk have vowed to take control of strategic infrastructure across the province they have declared an independent "people's republic".

Defying an ultimatum from Kiev to surrender, about two dozen separatist leaders gathered for a meeting in a top-floor room of the 11-storey building they have held for eight days.

"Everything from city cleaning to the sewage system, the airport, railway stations, military ... should all be under your control," Vladimir Makovich, one of the leaders, told the group.

Donetsk province has a population of 4.3 million residents – 10% of Ukraine's population – and much of the country's heavy industry. It is the biggest prize of the eastern regions in which pro-Russian separatists have captured government buildings during the past week.

As a 9am deadline passed, with no sign of the protesters leaving barricades in Donetsk or Slaviansk on Monday, at least 100 pro-Russian separatists attacked the police headquarters in the eastern city of Horlivka. Video footage shown on Ukrainian television showed ambulance staff said to have been called to treat the injured.

The standoff looked set to continue into the weekend as the latest round of talks between local, regional and protest leaders ended on Monday afternoon without agreement.

In Slaviansk, protesters – who woke on Monday anticipating an "anti-terrorist" operation involving the Ukrainian army that has not yet come – called on the Russian president, Vladimir Putin, to help them while Ukraine's acting president, Oleksandr Turchynov, asked for the deployment of UN peacekeepers.

Following the death of a state security officer and the wounding of two others near Slaviansk on Sunday, Turchynov gave a televised address in which he promised amnesty to those who had not fired at security forces if they laid down their arms and vacated government buildings.

In an emergency meeting soon after of the UN security council in New York, Russia described Ukraine's threat to mobilise armed forces as a "criminal order".

In Donetsk on Monday, Denis Pushilin – self-proclaimed head of what he called a "people's republic"– vowed to occupy the government building that has been the separatists' base until their demands for independence had been met. He claimed Turchynov was a war criminal for announcing an anti-terrorist operation against protestors, adding: "Now he's bringing enemy troops here, not to keep the peace but to attack."

Turchynov has maintained that the "anti-terorrism" offensive will go ahead, even though he sacked the state security chief in charge of the operation, signalling possible discord behind the scenes. According to the presidential website, Turchynov suggested to in a telephone call to the UN secretary general, Ban Ki-moon, that an "anti-terrorist operation" could be conducted jointly by Ukrainian security forces and UN peacekeepers.

He also took a risky step to try to undercut rebels' demands, by holding out the prospect of a referendum on the future shape of the Ukrainian state. He suggested this could be held at the same time as a presidential election on 25 May.

Pro-Russian protesters seized more government buildings in several cities in Donetsk on Sunday, actions for which locals have claimed credit. Kiev and Washington have blamed Russia for inciting the takeovers.

The European Union on Monday threatened Russia with more sanctions over its actions in eastern Ukraine, which Britain said was being destabilised by Moscow, although some EU states said diplomacy should be given more time.

Protesters, many of whom are armed, have been occupying an administration building in the regional capital, Donetsk, and a security service building in neighbouring Luhansk region for more than a week, and this weekend took over several buildings in Slaviansk and nearby cities. On Monday morning, Sergey Taruta, the Kiev-appointed governor of Donetsk, said an "anti-terrorist operation" was under way in the region and called on citizens "not to react to provocations", but Slaviansk and the capital appeared to be quiet.

Also on Monday, the Ukrainian security and defence council head, Andriy Parubiy, said intelligence services had detained Russian secret agents in Ukraine, but did not provide further details.

The pro-Kiev analyst Dmitry Tymchuk, a Ukrainian army and defence ministry veteran, wrote on Facebook on Monday that Russian intelligence services had created "agent networks" in Ukraine in 2010-13, laying the groundwork for the "saboteurs and co-ordinators from Russia".

Sergei Lavrov, Russia's foreign minister, said on Monday that no Russian agents were in eastern Ukraine. He said any powers that encouraged Kiev to use force against protesters must take full responsibility for their actions.

Sunday saw the first deaths in the burgeoning crisis in eastern Ukraine, where a majority speak Russian as their first language. The Ukrainian interior minister, Arsen Avakov, said one state security officer had been killed and five wounded in an operation in Slaviansk on Sunday, and the Russian news agency RIA Novosti reported that one pro-Russian activist had been killed.

The Guardian found evidence of shootouts in Slaviansk on Sunday, including a clash between government troops and unknown men on a road outside the city.

A video of the aftermath of the gun battle showed a wounded man in camouflage and a man in a black uniform with a machine gun, apparently dead. A witness said the man in the black uniform was a provocateur who had tried to spur the reluctant troops to attack civilians, but other video from Slaviansk showed Ukrainian forces dressed in similar black uniforms in a standoff with unarmed locals.

Troops ultimately pulled back without moving into the city, where locals continue to occupy a police station and a security service building.

Both the US and Nato have accused Russia of staging another Crimea-style intervention. Samantha Power, the US ambassador to the United Nations, said events were following the same pattern as in the Black Sea peninsula, where unidentified military forces took over government installations before the area was in effect annexed last month.

"[The unrest] is professional, it's co-ordinated, there is nothing grassroots-seeming about it. The forces are doing, in each of the six or seven cities they have been active in, exactly the same thing. Certainly it bears the telltale signs of Moscow's involvement," Power told ABC's This Week programme.

The Nato secretary general, Anders Fogh Rasmussen, described the protests as "a concerted campaign of violence by pro-Russian separatists, aiming to destabilise Ukraine as a sovereign state".

He said the appearance of men carrying Russian weapons and wearing uniforms without insignia was a "grave development" and called on Russia to pull back its troops from Ukraine's border.