Russian Prime Minister Vladimir Putin on Thursday accused the United States of supporting street protests against last Sunday’s elections and blasted Secretary of State Hillary Rodham Clinton for suggesting that the voting was rigged.

In Brussels, meanwhile, Russian officials said the NATO alliance was trying to bully Moscow into participating in a Europe-based missile defense system, which Moscow fears could be used against Russia. The United States says the system is intended to curtail threats from elsewhere.

Putin accused Clinton of declaring the vote unfair even before hearing from election watchdogs. He also expanded an attack he began last month on Golos, Russia’s only independent election monitor, which has raised serious questions about the legitimacy of the balloting. The organization receives aid from the United States and Europe.

If foreign countries want to send medicine or other humanitarian aid, that is fine, Putin said. But, he warned, those countries should stay away from politics.

“We need to safeguard ourselves from this interference in our internal affairs and defend our sovereignty,” Putin said. “It is necessary to think about improving the law and toughening responsibility for those who take orders from foreign states to influence internal political processes.”

Clinton, in Brussels at a meeting of NATO foreign ministers, tried to strike a conciliatory note, but did not back away from her earlier critiques of election irregularities.

“We value our relationship with Russia,” Clinton said. “At the same time . . . we expressed concerns that we thought were well-founded about the conduct of elections. And we are supportive of the rights and aspirations of the Russian people to be able to make progress and realize a better future, and we hope to see that unfold in the years ahead.”

Putin was making his first public remarks since his United Russia party won a sharply reduced parliamentary majority on Sunday. Election observers have said that widespread fraud probably concealed an even lesser result for the party, which has ruled Russia for the past 12 years. The prime minister was addressing the Coordinating Council of the Popular Front, a movement he organized in May as it became clear that United Russia was not generating much voter enthusiasm. The Popular Front includes United Russia but goes beyond it, drawing in popular figures and various organizations such as trade unions and student groups, some of which were surprised to find that they had been signed up.

Sunday’s election results and the allegations of fraud triggered some of the largest opposition protests in Russia in years, with hundreds of people arrested Monday and Tuesday. In his remarks, Putin said Clinton had “set the tone for some opposition activists, gave them a signal . . . and [they] started active work.”

Russia remains extraordinarily sensitive to remarks directed its way from the United States, and responds angrily when it considers the United States to be lecturing or patronizing it. “We are a major nuclear power and remain such,” Putin said. “And this causes some concerns for our partners.”

The prime minister indicated that Russian authorities — with 50,000 police and troops on the streets in Moscow and St. Petersburg — might escalate the crackdown on those who oppose the government.

In Brussels, Russian Foreign Minister Sergei Lavrov also used tough rhetoric to explain his country’s concerns about the U.S.-initiated missile defense program.

“They say there’s no need for discussion,” Lavrov told reporters after a meeting of the NATO-Russia Council. “They say, ‘This is the best possible option. . . . No, no, this is the best way, it’s not targeted against you.’ . . . We’d like our partners [in NATO] to have respect for our intellectual capability.”

The council was organized 10 years ago, but cooperation stalled in 2008 after Russia moved troops into breakaway regions of Georgia, a former Soviet republic. Talks have since resumed and were boosted last year when NATO invited Russia to join a new “strategic partnership” with the West, and to participate in a missile defense system it says is designed to fend off attacks from the Middle East — and Iran in particular.

But NATO-Russian negotiations over how the alliance would work are running into obstacles, with Russia expressing particular concern over an agreement by Turkey, among other NATO members, to host components of the system on its territory.

The northern-based Turkish radar “will be duplicating existing radar” in the southern part of that country, Lavrov said, and “covering a substantial part of Russian territory.”

Russia has demanded what it calls a “signed agreement” that the system will never be pointed at Russia or used to interfere with Russian defenses.

In a Thursday news conference after the meeting but before Lavrov spoke, NATO Secretary General Anders Fogh Rasmussen said that the alliance has listened to his concerns. “I hope Mr. Lavrov has also listened to NATO concerns,” he said.

Rasmussen on Wednesday evening said the disagreement reminded him of “confrontations of a bygone era,” a reference to the Cold War period of NATO’s origins.

Clinton, who headed the Obama administration’s delegation to the NATO session, said that the kind of “legally binding” guarantee that Russia demands would not happen. At the same time, she emphasized that the missile defense system was no longer motivated by a need to counter a threat from Russia.

“No country in the alliance is going to give Russia or any other country a veto . . . against the threats that we perceive are the most salient,” Clinton said. The system, she added, is “not directed at Russia; it is not about Russia. It is, frankly, about Iran, and other state and non-state actors that are threatening to develop missile technology.”

Clinton said NATO and Russia are cooperating on supply routes and other important strategic issues and must “keep working to try to forge agreement” on missile defense.

“We always said we wanted it to be an all-weather forum,” she said. “So when times are good, we have a chance to share our views, and when there are issues to be resolved, we will not shy away from doing so.”

Rasmussen said that NATO had offered the Russians written assurances that the system is not aimed at them and will not be used against them. “We know that if we can reach agreement on this issue, it will take our relationship to a new level,” he said.

U.S. officials have said that the European part of the system would begin to become operational by the next NATO summit in May, “with or without” Russian participation.

DeYoung reported from Brussels.