The Senate approved by voice vote Tuesday a resolution condemning Hezbollah and Hamas and their state sponsors, which include Syria and Iran, and supporting Israel's exercise of its right to self-defense.

"I applaud my Senate colleagues for their overwhelming support of this resolution, which reaffirms America's support for the State of Israel in its fight against Hezbollah and Hamas terrorists who continue to target Israeli soldiers and civilians," said Senate Majority Leader Bill Frist, R-Tenn., who added that the recent outbreak of violence started with "unprovoked attacks" on Israel by the terror groups.

"The Senate has spoken loud and clear: Israel has the right to defend itself against aggression. While I urge the Israeli government to act carefully, there should be no doubt as to where we stand in this conflict," Frist said.

The Republican-run House is eyeing a vote on Wednesday on a similar resolution supporting Israel's right to defend itself, condemning Hezbollah's rocket and missile attacks on northern Israel and backing early White House moves to cope with the crisis.

"Be it resolved that the House of Representatives reaffirms its steadfast support for the state of Israel; further condemns Hamas and Hezbollah for cynically exploiting civilian populations as shields ... calls for the immediate and unconditional release of Israeli soldiers held captive by Hezbollah and Hamas; (and) affirms that all governments who have provided continued support to Hamas or Hezbollah share responsibility for the hostage-taking and attacks against Israel and, as such, must be held accountable for their actions," reads a draft copy of the resolution being considered in the House.

House leaders had hoped late Monday the bipartisan resolution would be ready for floor action on Tuesday, but extensive redrafting has delayed action until Wednesday, senior GOP officials told FOX News.

Senior congressional Democrats said negotiations have been productive and they expect strong bipartisan support for the final resolution. Sources on both sides describe the House resolution as "pro-Israel" but note that it laments bloodshed among civilians and combatants in Israel and Lebanon.

In the Senate, Armed Services Committee Chairman John Warner, R-Va., had expressed reservations about the resolution's language, saying that it must take into account U.S. diplomatic efforts, the well-being of Americans in the region and the possible effect of violence on American involvement in Iraq and Afghanistan.

"Our support for Israel is very strong, Mr. President, but it cannot be unconditional," Warner said on the Senate floor late Monday.

Regardless of U.S. support for any party in the conflict, neither side appears ready to compromise. Still, a diplomatic solution is not out of the question. Lebanese Prime Minister Fuad Siniora met with U.N. Secretary-General Kofi Annan's adviser on Monday to discuss a path to compromise.

U.S. Secretary of State Condoleezza Rice is also headed to the region to try to forge a halt to the violence. Israeli Ambassador to the United Nations Dan Gillerman told FOX News that Rice will arrive in his country on Friday after a visit to the United Nations on Thursday. A State Department official categorically rejected the travel plans to the Mideast, though he did not deny that Rice is going to New York.

FOX News' Trish Turner and The Associated Press contributed to this report.