President Bush and British Prime Minister Tony Blair teamed together Friday to call on Syria to help end the growing fighting between Israel and Hezbollah military forces in southern Lebanon.

"My message to Syria is: You know, become an active participant in the neighborhood for peace," Bush said during a joint press conference at the White House with his British counterpart.

The two leaders also told reporters they were going to pursue a U.N. Security Council resolution to create a multinational force to aid the Lebanese government in taking control of Hezbollah guerillas and bring peace to the region. Britain and the United States hope a U.N. resolution could be in place by next week.

Bush said any resolution should provide "a framework for the cessation of hostilities on an urgent basis and mandating the multinational force."

Blair added: "Provided that is agreed and acted on, we can indeed bring an end to this crisis. But nothing will work unless, as well as an end to the immediate crisis, we put in place the measures necessary to prevent this occurring again."

Despite growing calls for an immediate cease-fire, Bush and Blair said they instead would move forward with plans for more long-term solutions.

"The prime minister and I have committed our governments to a plan to make every effort to achieve a lasting peace in this crisis," Bush said.

Bush also announced in the East Room news conference that Secretary of State Condoleezza Rice will be dispatched a second time on Saturday to the Middle East to continue diplomatic efforts to broker peace. Rice on Friday was in Indonesia meeting with Asian foreign ministers, but her return to the Middle East means the United States is continuing its push to resolve the violence.

It's also part of a western attempt to prevent broader conflict that some fear could draw in Syria, Iran and western nations.

"The message is very, very simple to them. It is that you have a choice. Iran and Syria have a choice," Blair said. "They can either come in and participate as proper and responsible members of the international community, or they will face the risk of increasing confrontation."

Bush also addressed Iran by saying: "Give up your nuclear weapons and your nuclear weapon ambitions."

CountryWatch: Israel | Lebanon | Syria | Iran

Bush and Blair also outlined a number of other actions that will be taking place in the coming days, including continued commitments to humanitarian efforts to aid hundreds of thousands of people displaced on both sides of the Lebanese-Israeli border.

Bush also noted: "The alliance between Britain and American is stronger than ever."

Israeli Ambassador Danial Ayalon agreed to the need to call in an international peacekeeping force, but said they must be strong enough to be able to defend themselves.

"It has to be a force which first and foremost can defend itself and then can enforce law and order in this very troubled land," Ayalon told FOX News. "So it has to be strong in terms big numbers, in terms of equipment, in terms of intelligence capabilities. And of course, it will have to have the cooperation and support of the Lebanese government, and the Lebanese forces themselves."

Former ambassador and special Middle East coordinator Dennis Ross said that what's needed is a solution that "doesn’t leave Hezbollah as a state within a state."

Ross said he did not believe Israel could disarm Hezbollah, but it's possible for an international force to give the Lebanese army the strength to keep Hezbollah contained.

In addition to foreign governments asking the close allies to use a heavy shoulder on Israel to stop its heavy attacks on Lebanese soil, a bipartisan group of senators were adding their voices into the mix Friday.

Sen. Debbie Stabenow, D-Mich., announced that she would introduce a resolution that "expresses support to attain a cessation in hostilities between Hezbollah and Israel," which is cosponsored by Sens. Christopher Dodd, D-Conn; Carl Levin, D-Mich.; and John Sununu, R-N.H.

"I believe it is time for us to assert our leadrership and put a stop to the violence as soon as possible. The innocent people of Lebanon and Israel have had enough ... of the violence and bloodshed. It is time for them to be able to live their lives in peace," Stabenow said.

Consultations continue on the makeup and mandate of a possible international peacekeeping force to stabilize the more than 2-week-old situation and supplement the Lebanese army. A senior State Department aide was meeting with European Union officials in Brussels and there were plans for talks at the United Nations as well.

White House press secretary Tony Snow expressed doubt that world leaders could come together on wording by next week.

The United States insists that any solution address long-standing regional disputes, particularly the call contained in a 2004 U.N. Security Council resolution that Lebanese militias such as Hezbollah be disarmed — something the Lebanese government has not done.

"It's all about getting the right conditions for that U.N. resolution," Snow said.

Snow suggested that one sensitive piece of the ongoing negotiations is which country would offer the resolution, to make it more likely to influence Hezbollah. But "to being talking about ongoing negotiations in some ways could jeopardize some of the things that are going on," Snow said.

U.S. officials say European troops would likely dominate any international peacekeeping force.

"I don't anticipate American combat power, combat forces, being used in this force," Rice told reporters Thursday while traveling to Malaysia for an Asian regional conference.

With Israel signaling it is settling in for a much longer battle than had initially been expected, Bush has suggested that he would support the offensive for as long as it takes to cripple the Shiite Muslim militant group. The fighting began after Hezbollah crossed the border and captured two Israeli soldiers. Defying some members of his own parliament, Blair has insisted that Hezbollah must first free the soldiers and stop firing rockets into Israel, a similar position to that taken by Bush.

Israel's punishing campaign of airstrikes, artillery shelling and clashes has killed an estimated 600 Lebanese. More than 50 Israelis have died, most of them soldiers.

Many countries in Europe and the Middle East are calling for an immediate cease-fire and have deplored the impact of Israel's campaign on Lebanon. The gap between the United States and Britain and other nations has intensified some of the diplomatic strains that have existed since Bush invaded Iraq in 2003 with Blair as one of his chief international backers.

Blair came to Washington for the second time in two months politically weakened, both by Iraq and by domestic woes in Britain.

Blair's government recently has had to deal with allegations that two U.S.-chartered planes carrying missiles to Israel stopped to refuel at a Scottish airport without filing the proper paperwork for hazardous materials. The missile dispute has added to questions about what Britain gets for its "special relationship" with the United States.

From Washington, Blair was to fly to California for meetings with business leaders.

The FOX News' Molly Hooper and Greg Simmons and The Associated Press contributed to this report.