US Secretary of State Antony Blinken and his Russian counterpart, Sergei Lavrov, have both described talks in Geneva on Ukraine as "frank".
The US is expected to put its position in writing next week, after which further discussions will be held.
There are fears that a huge Russian military force assembled near Ukraine's borders will be used to invade.
The US and its allies have threatened new sanctions, while Russia itself denies planning to attack.
With an estimated 100,000 Russian troops deployed near Ukraine, President Vladimir Putin has issued demands to the West which he says concern Russia's security, including that Ukraine be stopped from joining Nato.
He wants the Western defensive alliance to abandon military exercises and stop sending weapons to eastern Europe, seeing this as a direct threat to Russia's security.-BBC
