US Secretary of State John Kerry has said he has held a "frank meeting" with President Vladimir Putin during his first visit to Russia since the Ukraine crisis began in early 2014.
Both sides say that eight hours of talks between Mr Kerry and the Russian leadership were a welcome development.
It is the highest-level trip by a US official to Russia since the Ukraine crisis began.
Relations between the two countries deteriorated sharply since then.
The West has criticised Russia for annexing the Crimean peninsula and has accused Russia of arming rebels in eastern Ukraine.
Russia denies arming the rebels or sending troops there - although foreign minister Sergei Lavrov agreed with Mr Kerry at a joint press conference on Tuesday night that the ceasefire in Ukraine is still being violated.
More than 6,000 people have been killed in fighting which began in April 2014 between Ukrainian government forces and Russian-backed rebels in the eastern Donetsk and Luhansk regions.
Mr Kerry said it was critically important that a ceasefire deal agreed in Minsk in February be fully implemented in eastern Ukraine. He said US and EU sanctions against Russia could only be scaled down "if and when" that happens.
"We are in significant agreement on the most important issue of all, which is that [the conflict in Ukraine] will only be resolved by the full implementation of Minsk and all of us have responsibilities to undertake in order to affect that implementation," Mr Kerry said
Mr Kerry was speaking after holding four hours of talks with Mr Putin - in addition to talks with Mr Lavrov at the Black Sea resort of Sochi. Their negotiations also included Iran, Syria, Libya and Yemen.
He said it was necessary to keep the lines of communication open between the US and Russia as they addressed pressing global issues.
The Russian foreign minister and US secretary of state laid wreaths at a World War Two memorial earlier on Tuesday.
Mr Lavrov said at the joint press conference that the talks had helped Moscow and Washington understand each other better.
Earlier, he said that Russia was ready to co-operate with the US but only on an "equal basis" and without coercion.
A statement by Mr Lavrov on the foreign ministry website said that attempts to pressure Russia through sanctions would only lead to a "dead end".
State department spokeswoman Marie Harf said Mr Kerry's trip was "part of our ongoing effort to maintain direct lines of communication with senior Russian officials and to ensure US views are clearly conveyed".
Kremlin spokesman Dmitry Peskov praised Mr Kerry's decision to travel to Russia.