US Secretary of State Antony Blinken said the document, handed over in person by the US ambassador to Moscow John Sullivan, addressed Russia's concerns and raised those of the United States and its allies.
He told reporters the response sets out a serious diplomatic path forward, should Russia choose it, and has a principled and pragmatic evaluation of the concerns officials in Moscow have raised.
He added that the United States was open to dialogue.
"Putting things in writing is... a good way to make sure we're as precise as possible, and the Russians understand our positions, our ideas, as clearly as possible. Right now, the document is with them and the ball is in their court," he said.
The US has made clear that Russian demands for NATO to pull back troops and weapons from eastern Europe and bar Ukraine from ever joining the military alliance are non-starters but says it is ready to discuss other topics such as arms control and confidence-building measures.
Whether President Vladimir Putin is prepared to accept that limited agenda will determine the next phase of the crisis, in which Russia has massed about 100,000 troops near the border with Ukraine while denying it plans to invade.
In Paris, four-country talks dragged on longer than expected on ending a separatist conflict in eastern Ukraine, part of a wider crisis between Russia and Ukraine that has raised the risk of a full-scale war.
Earlier on Wednesday, responding to comments by US President Joe Biden that he would consider imposing sanctions personally on Putin, Russia said such a move would not hurt the Kremlin leader but would be "politically destructive".
Biden said on Tuesday personal sanctions on Putin, although a rare step, could be considered as part of a concerted drive by the US and its allies to convince Russia that any new aggression against Ukraine would bring swift and massive costs.
Kremlin spokesman Dmitry Peskov said US lawmakers discussing personal sanctions against Russia's top leaders were ignorant of the fact they were legally barred from holding assets, property and bank accounts abroad.
Putin's personal wealth is a sensitive topic in Russia.
According to his most recent official disclosure, he earned just shy of 10 million roubles ($US126,175) in 2020.
Peskov has previously said sanctioning Putin would amount to a severing of diplomatic relations.
Russia meanwhile staged new military drills on land and on the Black Sea and moved more paratroopers and fighter jets to Belarus, north of Ukraine, for what it describes as joint exercises there next month.
Foreign Minister Dmytro Kuleba said Russia had not yet massed sufficient forces for a large-scale offensive but that did not mean it could not do so later.
Blinken said US citizens in Ukraine should consider leaving.
Germany said it would supply Ukraine with 5000 military helmets, amid growing criticism of its refusal to join the US, UK and others in providing weapons to defend against Russia's much larger army.
The Czech government agreed to donate 4000 artillery ammunition rounds, sources told Reuters.
Kyiv mayor Vitali Klitschko told Bild newspaper the German delivery was a joke.
"What kind of support will Germany send next - pillows?," he said.
Much of Europe relies on Russia for around a third of its gas supplies.
Any interruptions to its Russian imports would exacerbate an existing energy crisis caused by shortages.
The US has been talking to major energy-producing countries and companies around the world over a potential diversion of supplies to Europe if Russia invades Ukraine.
Qatar's ruler will discuss the issue with Biden next week, a source told Reuters.
Responding to the uncertainty and the sanctions threats, Russia's rouble hit its lowest level against the US dollar since November 2020, having fallen more than 13 per cent in the last three months.
In Paris, officials from France, Germany, Russia and Ukraine were still locked in talks on the war in eastern Ukraine's Donbass region in which 15,000 people have been killed since 2014.
Andriy Yermak, chief of staff to Ukraine's President Volodymyr Zelenskiy, called the talks "a strong signal towards achieving peace in eastern Ukraine" but said major ceasefire violations were taking place.
In Russia's parliament, senior lawmaker Vladimir Vasilyev said the ruling United Russia party would ask the country's leadership to deliver unspecified military supplies to the two separatist regions.
Russia denies being a party to the Donbass conflict but senior Ukrainian sources say they estimate it has 2000 military personnel there, supporting about 35,000 separatists.
