The US has rejected Russia's demand to bar Ukraine from Nato, amid warnings Russia might invade its neighbour.
Secretary of State Antony Blinken was giving Russia a formal response to its demands to resolve the Ukraine crisis.
Mr Blinken gave no concessions but said that he was offering Russia "a serious diplomatic path forward, should Russia choose it".
Russia's foreign minister Sergei Lavrov said President Vladimir Putin would now assess Mr Blinken's response.
While the document - delivered by the US in coordination with the Nato military alliance - does not address Russia's "main concern" about the alliance's expansion, Mr Lavrov said it "gives hope for the start of a serious conversation" on secondary questions.
The president's spokesman Dmitry Peskov meanwhile told reporters Russia would not "rush into assessments", saying it would take "time to analyse" the response.
Russia had issued a written list of its concerns about the expansion of Nato and related security issues. Among them was a demand for Nato to rule out the possibility of Ukraine and others ever joining the alliance.