Correspondents had predicted that discussions would be difficult, despite recent conciliatory remarks from President Vladimir Putin on the need for negotiation over the issue.
A senior US official said that although the talks had been an important "first step", much remained to be done to overcome Moscow's opposition.
The talks come at the end of a tour of European capitals by the US delegation aimed at explaining Washington's plan to set up the $60bn missile interception system.
Correspondents had predicted that discussions would be difficult, despite recent conciliatory remarks from President Vladimir Putin on the need for negotiation over the issue.
Russian spokesman Alexander Yakovenko said that two hours of discussions at the Foreign Ministry had been substantive, but left "more questions than answers".
"The United States has been unable to convince us how to solve the problems of international security without damaging disarmament agreements," he said.
"But I want to underline that discussions will continue," he added.
The meeting was the first direct talks between Russia and the US about major strategic issues since President Bush took office.
'Rogue state' threat
The planned missile defence shield would destroy incoming missiles from so-called "rogue states" such as Iraq and North Korea, which the US argues represent the primary threat to the security of Washington and its allies.
Critics say the shield is technologically unproven, and could trigger a new arms race.
To introduce the system, the US would also have to set aside the 1972 Anti-Ballistic Missile treaty banning such systems.
But speaking last week, Mr Bush said: "We need a new framework that allows us to build missile defences to counter the different threats of today's world.
"To do so, we must move beyond the constraints of the 30-year-old ABM treaty."
Moscow suspicious
Moscow is deeply suspicious of the impact that missile defence would have on its own nuclear forces.
Members of the Russian parliament have accused the US of wanting to reinforce its domination of the world.
Last week President Putin emphasised the need for dialogue on the issue, but warned against destroying the existing international security system.
Analysts say the Russians want to be consulted, and also hope to extract concessions, such as cuts in the American nuclear arsenal.
Turkish visit
After Moscow, the US delegation's next stop was Turkey. Under Secretary of State Marc Grossman held talks with Turkish Prime Minister Bulent Ecevit and Foreign Minister Ismail Cem.
"We're in listening mode now. They're explaining and we're listening," said Turkish Foreign Ministry Under Secretary Faruk Logoglu after the talks.
Mr Grossman said it was too early to discuss whether Turkish bases would be used for the missile scheme.