Ukraine's president has effectively accused Russia of invading his country, saying troops have been moved across the border to support separatists now fighting on two fronts in the east.

"Recent Russian actions clearly demonstrate that Moscow is bluntly drawing Ukraine and the entire world into a full-scale war," Ukraine's foreign ministry said in a statement.

Petro Poroshenko, the president, cancelled a planned trip to Turkey and demanded an urgent meeting of the UN security council after the six-month crisis deepened with reports of fresh Russian incursions along Ukraine's south-eastern coast.

"Russian forces have actually entered Ukraine," he said in a statement. The accusation comes just two days after the Ukrainian leader met Vladimir Putin in Minsk, since when the situation in the east has deteriorated.

Poroshenko stopped short of calling the movements an outright invasion, but convened an urgent meeting of the country's national security council to discuss the Russian moves. "I have made a decision to cancel my working visit to the republic of Turkey due to sharp aggravation of the situation in Donetsk region, particularly in Amvrosiivka and Starobeshevo, as Russian troops were actually brought into Ukraine," he said. "The president must stay in Kiev today."

In Brussels, a Nato military officer told Reuters that the alliance believes there are now more than 1,000 Russian soldiers fighting in Ukraine. Russia has repeatedly denied it is fighting in Ukraine, and speaking after the Minsk negotiations, Putin said that a solution to the crisis in east Ukraine is "not our business; it is a domestic matter for Ukraine itself". He said all Russia could do was "support the creation of an environment of trust".

Putin's words, however, jar sharply with events on the ground. Fighters and weapons have long been able to move freely along the unguarded sections of Russia's border with Ukraine, and reporters in Novoazovsk near the border with Russia say what appears to be hastily repainted Russian military hardware has appeared in the town in recent days. Ukrainian officials have described the town as under control of the Russian military.

Russia's denials appear increasingly flimsy. When the Guardian saw a Russian armoured column cross the border two weeks ago, the foreign ministry and local security services denied any incursion had taken place, saying it was a border patrol that had not strayed into Ukrainian territory.

Earlier this week, when 10 Russian paratroopers were captured well inside Ukraine, sources in the defence ministry also said they had been part of a border patrol that had got lost and entered Ukraine "by accident".

The head of the self-declared Donetsk People's Republic, Alexander Zakharchenko, admitted on Thursday that there are serving Russian soldiers among his fighters, but claimed they were volunteers who were taking a holiday in the region.

"Among the Russian volunteers there are many former soldiers, who are fighting alongside us and understand that it's their duty," said Zakharchenko in an interview with Russian television. "And moreover, I'll say it openly, we also have current soldiers, who decided to take their holidays not on the beach, but among us."

Black smoke billows over fire after shelling in Novoazovsk. Photograph: Alexander Khudoteply/AFP/Getty Images

Although Putin's actions in Ukraine have been supported by the vast majority of Russians, there is increasing dissent inside the country about the growing evidence of a stealth war. Mikhail Khodorkovsky, formerly Russia's richest man – who was released from jail late last year – said Russians should not be silent about the country's soldiers being killed in Ukraine and secretly buried.

"We are fighting in Ukraine, fighting for real," the former oligarch wrote. "Our authorities are always lying about this, in the '80s about Afghanistan, in the '90s about Chechnya and now about Ukraine. Why are we remaining silent? Have we become cowards? Are we scared of even thinking now?"

There have also been appeals from relatives of the soldiers captured in Ukraine, calling on Putin and the defence ministry to help bring the men home alive.

Kiev on Thursday called on its western allies for more support. The foreign ministry said in a statement: "Under the current circumstances, Ukraine counts on serious support from its international partners and believes that strengthening EU sanctions against Russia as well as providing Ukraine with military and technical support will help deter Russian aggression."