U.S. lawmakers, including the Democratic and Republican presidential candidates, condemned Russia’s invasion Friday of neighboring Georgia and called for diplomatic efforts to settle the nations’ differences.

Senate Foreign Relations Committee Chairman Joseph R. Biden Jr., D-Del., called on Russia to restore order in the region. He characterized the violence as “a grave threat to regional security.”

“I welcome Georgian President Mikheil Saakashvili’s call for calm and restraint, and strongly encourage South Ossetians, along with the Russian peacekeepers who ostensibly maintain order in the area, to bring an immediate end to the fighting,” Biden said. “The world will be watching — and expects Russia to live up to its commitments.”

Georgia said it sent troops into South Ossetia to end the breakaway region’s self-proclaimed independence, which it first asserted in 1992 after a roughly two-year war.

Russia said it invaded the region with armored units and combat aircraft to protect South Ossetians from ethnic cleansing at the hands of Georgians. The invasion comes against the backdrop of Russian resentment over NATO’s consideration of Georgia as a possible new member.

To varying degrees, the U.S. lawmakers who weighed in on the crisis depicted Russia as the unwarranted aggressor and put the onus on Moscow to restore order. They also echoed the Bush administration’s call for a withdrawal of Russian troops from Georgia’s territory.

“Since the fall of the Soviet Union nearly two decades ago, Russia has intimidated its neighbors and tried to establish hegemony over former Soviet states such as Georgia — and today’s action is another manifestation of that,” House Majority Leader Steny H. Hoyer, D-Md., said in a statement. “The international community should unequivocally demand that Russia immediately withdraw its forces from Georgian territory, and should lead an effort to resolve the conflict in South Ossetia and seek a broader peace where differences are addressed through negotiation not violence.”

Republicans, including House Minority Leader John A. Boehner, R-Ohio, expressed concern that Russia’s actions were a dangerous sign of Moscow’s intentions.

“I’ve been concerned about the Russians for the last several years,” he said. “They’re going through a dramatic change over there — new leadership — and appear to be insistent on flexing their muscles. I would hope that they would respect the areas that were part of the former Soviet republic, respect the wishes of those local jurisdictions.”

Rep. Ileana Ros-Lehtinen of Florida, ranking Republican on the House Foreign Affairs Committee, called for a complete reappraisal of U.S.-Russian relations.

She also called on President Bush to withdraw a civilian nuclear cooperation deal with Russia submitted May 13 to Congress. The Foreign Affairs panel approved legislation (HR 6574) on July 24 that would green-light the deal, but only if Moscow scales back its aid to Iran.

Rep. Mike Pence, R-Ind., another member of the panel, said Russian military action in Georgia, which has a critical oil pipeline from the Caspian Sea and Central Asia to Europe and the United States, would spur oil prices upward. He said the crisis highlighted the need to support efforts by House Republicans to promote domestic oil drilling.

“It’s a very serious business,” Pence said. “Georgia is a transit point for the oil.”

As for the presidential candidates, Republican Sen. John McCain of Arizona said the United States should convene an emergency U.N. Security Council session to deal with the crisis.

“Russia should immediately and unconditionally cease its military operations and withdraw all forces from sovereign Georgian territory,” McCain said. “What is most critical now is to avoid further confrontation between Russian and Georgian military forces.”

McCain also urged a meeting of NATO to review measures it might take, and recommended a neutral peacekeeping force replace Russian troops in South Ossetia.

Sen. Barack Obama, D-Ill., called on both sides to exercise restraint.

“Georgia’s territorial integrity must be respected,” Obama said in a statement. “All sides should enter into direct talks on behalf of stability in Georgia, and the United States, the United Nations Security Council, and the international community should fully support a peaceful resolution to this crisis.”

Obama had spoken about the gathering tensions July 23, issuing an extensive statement urging calm, not only in South Ossetia but also in Abkhazia, another breakaway region of Georgia. The statement made clear that Obama thinks Russia bears the most responsibility for the tensions and expressed support for Georgia’s “right” to pursue NATO membership.

Obama said the U.S. commitment to Georgia’s sovereignty “will not change under an Obama administration.”

Meanwhile, the White House said President Bush had discussed the situation with Russian Prime Minister Vladimir Putin in Beijing, where both leaders watched the opening of the Olympic games.

“We urge all parties, Georgians, South Ossetians and Russians, to de-escalate the tension and avoid conflict,” White House press secretary Dana Perino said. “We are working on mediation efforts to secure a cease-fire and we are urging the parties to restart their dialogue.”

Secretary of State Condoleezza Rice called representatives of Georgia and Russia, urging restraint, and made plans to send a U.S. envoy to the region.

Finnish Foreign Minister Alexander Stubb, chairman of the Organization for Security and Co-operation in Europe, who had warned of the risk of war in the region in meetings with U.S. officials in Washington last month, said in a statement that the crisis must be defused quickly.

“I urge the Georgians, South Ossetians and Russians to cease fire, end military action and stop further escalation,” he said. “We need to pull back from the brink of a full-fledged war.”

In another consequence of the fighting on U.S. policy, Georgia announced it will withdraw 1,000 soldiers from Iraq to help fight off Russian forces in South Ossetia.

Edward Epstein, Kathleen Hunter and Josh Rogin contributed to this story.