Russia has told the United States that it had no plans to invade Ukraine, as the two sides agreed to more efforts to keep tensions from turning into a full-blown confrontation.

After more than seven hours of negotiations in Geneva on Monday, the Russian and US negotiators both offered to keep talking, though there was no sign of a major breakthrough.

Russian Deputy Foreign Minister Sergei Ryabkov said he had assured his US counterpart, Deputy Secretary of State Wendy Sherman, that those fears were unfounded.

"We explained to our colleagues that we have no plans, no intentions to 'attack' Ukraine ... There is no reason to fear any escalation in this regard," he told reporters after the talks.

Ryabkov said the United States "took Russian proposals very seriously" and that Moscow was "for the continuation of dialogue".

Sherman said that she offered to make reciprocal moves with Russia on missiles and exercises, but renewed warnings of major costs if Moscow invaded Ukraine.

"There will be significant costs and consequences, well beyond what they faced in 2014," when Moscow seized the Crimean peninsula and backed an insurgency in eastern Ukraine, she said.

READ MORE: NATO warns Russia of 'severe costs' of attacking Ukraine ahead of talks

Russian troop withdrawal

Sherman said the United States was ready to meet again, but that Russia had not offered assurances that it will pull back troops amassed near Ukraine.

She said she told her Russian counterpart to "return the troops to the barracks, or tell us what exercises are ongoing and what your purpose is."

Sherman also said she ruled out a Russian call for guarantees that Ukraine will not join NATO.

"We were firm, however, in pushing back on security proposals that are simply non-starters to the United States. We will not allow anyone to slam closed NATO's open-door policy."

The high-stakes negotiations came amid fears of a Russian invasion of its pro-Western neighbour Ukraine, and with Moscow demanding wide-ranging concessions from Washington and its NATO allies.

READ MORE: US, Russia take firm lines ahead of crucial Ukraine talks