The US will not allow Russia to stop it from deploying anti-missile defences in Europe, US Secretary of State Condoleezza Rice has said in Moscow.
Russia and the US defined their differences but did not resolve them
"I don't think anyone expects the United States to permit a veto on American security interests," she said after meeting President Vladimir Putin.
Earlier, they agreed to tone down the rhetoric in public exchanges.
These were the first talks since February when Mr Putin accused the US of seeking global dominance.
Washington is not seeking confrontation, but wants Moscow's co-operation over sensitive issues such as Kosovo, Iran and missile defence, the BBC's defence and security correspondent Rob Watson says.
But the agreement to tone down the rhetoric does not mask the continuing differences and the sense in Moscow that Washington has long been ignoring legitimate Russian concerns, our correspondent says.
Ms Rice held talks on Tuesday with Mr Putin, Russian Security Council Secretary Igor Ivanov, Foreign Minister Sergei Lavrov, former Prime Minister Yevgeny Primakov and Russian civic leaders.
The two sides are divided over several issues, including the missile defence shield plan.
She defended her position on US missile plans, saying: "The United States needs to be able to move forward, to use technology to defend itself, and we're going to do that."
But she also said: "If there are concerns about how the United States has and is continuing to exercise power, absolutely, we can have that discussion."
Russian Foreign Minister Sergei Lavrov said his country's "stance on missile defence was reaffirmed", but maintained it had been a "candid and friendly conversation".
"[Mr Putin] supported the understanding by the American side that rhetoric in public exchanges should be toned down and we should focus on concrete issues," local media quoted Mr Lavrov as saying after the talks.
And Ms Rice agreed that the two sides had talked "about the need to keep the temperature down".
The US opened talks with Poland on Monday over its plans to locate part of its defence shield on Polish soil.
The US wants 10 interceptor rockets there to destroy any long-range ballistic missiles fired at the US from the Middle East.
Warsaw has indicated it will back the plan if it improves Poland's security. The US also wants a radar base in the Czech Republic.
The Kremlin has also expressed opposition to Washington's backing for the independence of Kosovo from Serbia. Russia believes Kosovo should remain part of Serbia.
"It was agreed to search for a solution on Kosovo that would be acceptable for all, but there is no such solution immediately in sight," Russian Foreign Minister Sergei Lavrov said.
For her part, Ms Rice has criticised what she sees as democratic setbacks in Mr Putin's Russia.