Despite a recent uptick in bilateral dialogue, relations between Moscow and Washington are "lying on the floor", the Kremlin told Russia's RIA news agency, amid Western objections to ongoing major Russian military drills near its borders with Ukraine.

The United States on Sunday said Russia could invade Ukraine at any time and might create a surprise pretext for an attack, as it reaffirmed a pledge to defend "every inch" of NATO territory.

Russia has more than 100,000 troops massed near Ukraine, has repeatedly denied any plans to invade and has accused the West of "hysteria".

Kremlin spokesperson Dmitry Peskov said there were certain channels for dialogue, one positive being that President Vladimir Putin and his US counterpart Joe Biden have been in contact - the two spoke by phone on Saturday - but that ties in other areas were strained.

"The heads of state are in dialogue, there is dialogue on other fronts," RIA cited Peskov as saying in an interview. "This is a plus because you know that just a couple of years ago there was zero dialogue, there were no such contacts whatsoever.

"But on the rest, unfortunately, in bilateral relations one can only talk about negatives. We are at a very, very low point. They are actually lying on the floor."

Russia is engaged in major joint military drills with Belarus, Ukraine's northern neighbour. Sukhoi Su-30 fighter jet crews conducted a joint patrol flight along the border between Russia and Belarus on Monday, Russia's defence ministry said.

Russia will also send a detachment of ships armed with cruise and supersonic missiles from its Caspian Flotilla to the Black and Mediterranean Seas, the Izvestia daily cited military sources as saying.

Russia's Black Sea fleet on Saturday said more than 30 ships had started training exercises near the Crimean peninsula Moscow annexed in 2014, part of a sweeping set of exercises from the Pacific to the Atlantic involving all its fleets in January and February.

Meanwhile, over 30 transport and attack helicopters are engaged in tactical exercises in southern Russia, the military said on Monday.