Senator John McCain, Republican of Arizona, and Senator Christopher S. Murphy, Democrat of Connecticut, both members of the Foreign Relations Committee, appeared onstage at Independence Square and expressed American solidarity with the protesters’ goals.

“We are here to support your just cause: the sovereign right of Ukrainians to determine your own destiny,” said Mr. McCain, a former Republican presidential nominee, to much applause. He added: “The destiny you seek lies in Europe. Ukraine will make Europe better, and Europe will make Ukraine better.”

At a news conference later, Mr. McCain and Mr. Murphy said the Senate would consider imposing sanctions against the Ukrainian government should there be any further violence against protesters. Mr. Murphy said he had accompanied Mr. McCain here to show that there was bipartisan support for the Ukrainian demonstrators, and he said he was impressed by the peaceful nature of the rally.

While Mr. McCain chastised Russia for its role in derailing Ukraine’s plans to sign the trade and political accords with Europe, describing it as interference in Ukraine’s sovereign affairs, he said he saw no contradiction in standing onstage before a crowd that had called for the ouster of Prime Minister Mykola Azarov and his government. He called it “my duty to speak out” on behalf of the Ukrainian people and human rights.

Mr. Murphy also said it was clear that the protest movement had staying power. “We understand protesters on the square won’t go away until there are real reforms proposed by this government, or another government,” he said.