At least 70 Russian soldiers died this year in the fierce battles around Debaltseve, which resulted in a rout of Ukraine forces and the restoration of a vital supply line for separatist fighters, the report claims.

Another 150 died in eastern Ukraine last August, alongside separatists fighting to rebuff an advance by Ukraine government forces.

And there are currently up to 10,000 Russian soldiers still in eastern Ukraine supporting the separatists, despite the current Minsk ceasefire accord which is looking increasingly shaky.

The report, titled Putin. War, was released on Tuesday. It was based partly on interviews with families of Russian troops, Nemtsov's allies said.

It was intended to counter repeated Kremlin denials that it is directly involved in fighting in Ukraine.

The report claims separatist leaders in Ukraine are controlled by Vladislav Surkov, an aide to Russian President Vladimir Putin, Radio Free Europe reported.

"The Russian government provided active political, economic, personnel, and also direct military support to the separatists," the report says, according to an RFE/RL translation.

A spokesman for the Kremlin declined to comment on the report, saying he was not familiar with it and could not say if Russian President Vladimir Putin would look into it.

Nemtsov, a former deputy prime minister who became a fierce critic of the Putin regime, was shot dead in February, metres from the Kremlin walls.

He left behind materials including a table of contents, handwritten notes and other documents, which were compiled into the final report by writers including economists Sergei Aleksashenko and Alfred Koch, and journalists Aider Muzhdabayev and Oleg Kashin.

"I know what needs to be done," Nemtsov is quoted saying in the report. "We need to write a report 'Putin. War', publish it in large numbers and hand it out on the streets. We will tell how Putin unleashed this war. That's the only way to defeat propaganda."

However the report's authors struggled to find a printer who will distribute it in Russia on a large scale.

The report claims Moscow supports the separatists "to create an advantageous negotiating position with Western countries" so Russia can agree to help end hostilities in Ukraine in exchange for the lifting of sanctions imposed when Russian annexed Crimea last year.

The Kremlin has repeatedly denied any direct military involvement in Ukraine. It says Russians proven to be in Ukraine had crossed into the conflict zone as individual volunteers, and any Russian servicemen found there had resigned from the military before entering Ukraine.

The report said last year Russian soldiers' families were given 2 million rubles each ($45,000) after signing pledges not to reveal where their loved ones died.

However, the report claimed that Russia had started discharging troops from the army on paper before sending them into Ukraine – then refusing to pay compensation to their families.

According to the report, Russia has spent 21 billion rubles ($472 million) operating a force of 6000 'volunteer' soldiers in Ukraine, another 25 billion rubles ($561 million) funding local insurgents, and 7 billion rubles ($157 million) maintaining and repairing military hardware.

"The most important thing is to tell the truth," activist Ilya Yashin said at the report's launch in Moscow, Radio Free Europe reported. 
"The purpose of this report is to tell people the truth. The leadership of our country bears responsibility for a crime. It bears responsibility for an enterprise that has victimised Ukrainian citizens and our fellow Russian citizens."

Mr Yashin said the report's intended audience was "the entire Russian people".

"We want to tell people the truth about what is happening in Russia, about what is happening in eastern Ukraine. We want to catch Putin in his lies. We want to tell people that the president of Russia - a man who controls nuclear weapons and leads an enormous country - is lying to the Russian people and to the entire world," he said.

The Nemstov report is not the only one claiming Russian involvement in Ukraine.

The Atlantic Council, a Washington DC thinktank, has announced that in two weeks' time it will release a new report that "provides irrefutable evidence exposing the breadth and depth of Russian military involvement in Ukraine's east."

"Drawing upon publicly available information, the report documents the movement of Russian troops from training camps into Ukraine. It also demonstrates that many artillery strikes on Ukraine originate in Russia and examines the wide array of Russian military equipment in the hands of so-called separatist forces," the Council said in a press release.

US Secretary of State John Kerry landed in Sochi in Russia on Tuesday, for talks with Mr Putin and Russian Foreign Minister Sergei Lavrov.

It was Kerry's first visit to Russia in two years, and was seen as a sign that both sides wanted to rebuild bridges after the annexation of Crimea and the conflict in Ukraine.

They were due to discuss Ukraine as well as the crisis in Syria and the Middle East.

Mr Lavrov presented Mr Kerry with baskets of tomatoes and potatoes.

Their meeting lasted more than four hours, according to reports, before the meeting with Mr Putin.

- With Reuters, Bloomberg