President Vladimir Putin said Tuesday that Russia's security concerns had been ignored as tensions rage between Moscow and NATO over Ukraine.

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

"But it is already clear that fundamental Russian concerns ended up being ignored," Putin said, in his first significant public remarks in weeks on the crisis sparked by fears of a Russian invasion of Ukraine.

After Russia put forward sweeping security proposals, having sent tens of thousands of troops to Ukraine's border, the United States late last month delivered a reply in coordination with NATO allies.

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.

"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.

But, he said, that 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."