The U.S. Senate and House of Representatives are preparing to vote this week on resolutions backing Israel and condemning Hezbollah, which last week kidnapped two Israeli soldiers, sparking violence across the Israel-Lebanon border.

The Republican-run House is eyeing a vote on Wednesday on a 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.

Meanwhile, on the Senate side of Capitol Hill, a similar resolution is being drafted to offer support for Israel against its longtime enemies. A vote was scheduled for late Tuesday.

β€œThe governments of Iran and Syria are infiltrating places like Lebanon with support for Hezbollah and Hamas," said Sen. Kay Bailey Hutchison, R-Texas, who co-sponsored the Senate resolution condemning Hezbollah and supporting Israel's right to self-defense against it and the Palestinian militants that are also fighting the Israelis.

"All of those terrorist organizations have sought to destroy [Israel] and yet, it has in the middle of this, stood as a democracy, a democratic form of government, a free economy hoping to trade with other people in the region and certainly trading in the world. ... They should have the support of the unified world community in saying to the terrorists and to the governments that are supporting the terrorists β€” Hamas and Hezbollah, Iran and Syria β€” that the world is not going to sit by and let people be terrorized,” Hutchison said.

Resolutions only express the sense of the chambers and have no enforcement mechanism, but neither statement shies away from stating support for Israel's right to defend itself and blaming Iran and Syria for contributing to the conflict.

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.

Rep. John Dingell, D-Mich., the longest-serving Democrat in the House, said that in order for a U.N.-led peacekeeping effort to occur, "Israel must immediately cease inflicting further damage on Lebanon's civilian infrastructure."

"Failure to do this will have appalling consequences," he said, adding that Israel's response to the killings and captures have been "disproportionate and counterproductive" and could lead to general war in the Middle East and possibly World War III.

Dingell also said that the United States must bring about a cease-fire.

"We must be a honest broker and reliable friend to all who want peace," he said.

In the Senate, Armed Services Committee Chairman John Warner, R-Va., expressed reservations about who is right and wrong in the current conflict, saying that U.S. diplomatic efforts, the well-being of Americans in the region and the effect the violence could have on American involvement in Iraq and Afghanistan must be reflected in the Senate resolution.

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

Still, other senators have offered seemingly unconditional support for Israel, which has long defended its right to exist against Arab and Muslim states that have called for its destruction.

"We cannot listen to those who define how strong the response ought to be. It's up to Israel to decide how strong her response ought to be," said Sen. Frank Lautenberg, D-N.J.

"We will support [Israel's] efforts to send a message to Hamas, Hezbollah, to the Syrians, to the Iranians, to all who seek death and domination instead of life and freedom," said Sen. Hillary Rodham Clinton, D-N.Y. Both senators appeared at a rally of Jewish organizations sponsored by the United Jewish Communities.

Regardless of support for any party in the conflict, neither side appears ready to compromise. In an address to the Israeli Parliament on Monday, Prime Minister Ehud Olmert said Israel will not cease its military operations until the kidnapped soldiers are returned and Lebanese troops control the southern region where Hezbollah now freely operates.

A spokesman for Hezbollah, listed on the State Department's roster of terrorist organizations but holding a sizable minority of seats in the Lebanese Parliament, accused foreign envoys of procrastinating while Israel continues to bomb strategic positions like the Beirut airport and major highways in Lebanon.

Hezbollah parliamentarian Hussein Haj Hassan said Monday that Israel's conditions for a ceasefire are unacceptable.

The international envoys have conveyed Israeli conditions. These conditions are rejected," Hassan told Al Jazeera television. "We accept what secures our country's interest and pride and dignity and not to submit to Israeli conditions."

But 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, the State Department announced Monday.

FOX News' Major Garrett and Jim Angle and The Associated Press contributed to this report.