The West has ignored Russia's security concerns, Russian President Vladimir Putin said Tuesday amid soaring tensions between Moscow and NATO over Ukraine.

"We are carefully analyzing the written responses received from the United States and NATO," Putin told reporters following talks with Hungarian Prime Minister Viktor Orban.

"But it is already clear that fundamental Russian concerns ended up being ignored," Putin stated, speaking for the first time in weeks about the crisis prompted by Western fears of an imminent Russian invasion of Ukraine.

Kyiv and Moscow have denied the western fearmongering, saying there was no such invasion anywhere on their radars.

Moscow has been demanding a written commitment that Ukraine would never be able to join NATO and that the alliance would not place any strategic military equipment in certain countries in the region surrounding Russia.

The United States late last month delivered a reply in coordination with NATO allies, and Russia has since then stressed that its concerns had been ignored.

The United States rejected Russia's demand to bar Ukraine from NATO but offered what it called a new "diplomatic path" out of the crisis. 

"We did not see adequate consideration of our three key demands regarding the prevention of NATO expansion, the refusal to deploy strike facilities near Russia's borders, and the return of the bloc's military infrastructure in Europe to the state in 1997," Putin said. 

Putin had previously said NATO was backtracking its military capacity and infrastructure in Europe to the position of 1997 when the Founding Act between Moscow and Brussels was signed.

"When ignoring our concerns, the US and NATO point to the right of states to freely choose how to ensure their security," the Russian leader added, which he highlighted was just one part of the security equation.

"The second integral part says that it is impossible to allow the strengthening of one's security at the expense of the security of others," in reference to the US and NATO bolstering allies in Europe, which are on the borders with Russia.

Read: US scrambling to deliver arms to Ukraine

Putin hopes for solution to Ukraine crisis, 'not simple'

President Vladimir Putin said he hoped Russia and the West could find a solution to the security crisis over Ukraine and accused Washington of using Kyiv as a tool against Moscow.

"I hope that in the end, we will find a solution, although it will not be simple," Putin said.

He added Washington's main goal was to contain Russia rather than protect Ukraine.

"It seems to me that the United States is not so much concerned about the security of Ukraine... but its main task is to contain Russia's development," Putin said

"In this sense, Ukraine itself is just a tool to reach this goal. This could be done in various ways," he said, noting that this could be done by getting Russia involved in an armed conflict.

"Let's imagine that Ukraine is a NATO country and begins a military operation in Crimea, on Russia's sovereign territory," Putin said. "What, do we have to fight the NATO alliance? Did anyone think about that? Looks like no."