President Bush reaffirmed his support Monday for U.S. troop and NATO operations in Afghanistan, saying the welfare of that nation is critical to the security of the international community.

The meeting between Bush and NATO Secretary-General Jaap de Hoop Scheffer, the head of the U.S.-European military alliance, at the president's ranch in Crawford, Texas, came as fresh violence broke out throughout the Middle East and in Afghanistan.

Over the weekend, suicide bombers in Afghanistan killed a total of 19 people in two separate attacks — one on Saturday in the province of Paktia and one Sunday in the city of Kunduz. The Taliban claimed responsibility for both attacks. Among those killed over the weekend were three German soldiers operating under the NATO flag.

"We're involved in an ideological struggle; that these murderers -- these radicals, these extremists -- have got a point of view. If you want to find out what their point of view is about, look what happened in Afghanistan under the brutal relationship of the Taliban and Al Qaeda," Bush said.

"If we discuss Afghanistan, I should start by saying that we, the international community, NATO forces, U.S. forces, are there to help rebuild and develop that nation. That nation deserves to be developed and to be rebuilt. But we are there for another reason as well: Afghanistan is still one of the front lines in our fight against terrorism. And it is my strong conviction that that front line should not become a fault line," Hoop Scheffer said.

But the violence is not contained to Afghanistan. In Lebanon, violence erupted again Monday when Lebanese army artillery shelled a Palestinian enclave where a group suspected of ties to Al Qaeda is holed up. Local officials describe the fighting, which began over the weekend, as the worst eruption of violence since the end of the 1975-90 civil war.

Senior administration officials told FOX News that Bush wants to emphasize U.S. support for the "legitimate and democratically-elected" government of Lebanese Prime Minister Fuad Saniora. The official said this administration "supports the Lebanese government as it faces down the threat of terrorism and political violence in that country."

"This violence demonstrates why the international community needs to remain engaged in helping the Lebanese government fulfill its international obligations under U.N. resolution 1559 to rid the country of armed militias and terrorists," the official said.

The same official wouldn't say whether it is thought that the terrorists inside this camp near Tripoli, Lebanon, are tied to Syria, but the administration continues to have multiple concerns about Syrian efforts to try to topple the Lebanese government.

The official also said Fatah-al Islam, the militants fighting the Lebanese army, have "clear ties to Al Qaeda" but questions remain about whether the fighting there is the result of an Al Qaeda-launched terrorist action.

As to NATO's mission in Afghanistan, White House deputy spokesman Tony Fratto stressed the importance of extending military assistance beyond the North Atlantic region. NATO has 37,000 troops from 26 countries — 15,000 from the United States — working in Afghanistan, its largest mission ever.

It is "incredibly important to America's security interests" that NATO continue its work, Fratto said.

The NATO secretary-general's visit to the ranch is his first. The last time the two leaders met was at the NATO Summit in Riga, Latvia, in November. Hoop Scheffer visited the White House last October ahead of that meeting.

At the meeting in Latvia, Bush stressed the importance of NATO's European partners participating in calming the the more volatile southern region of Afghanistan.

"I pledged to the secretary general we'll work with our NATO allies to convince them that they must share more of the burden and must all share the risks in meeting our goal," Bush said Monday, echoing his earlier remarks.

Despite the struggle and an increase in violence in the region, both Bush and Hoop Scheffer have made a strong commitment to defeating the Taliban. In a visit to Pakistan last week, Hoop Scheffer reiterated that NATO has no plans to pull out of the region.

During their private talks, the two also agreed to transform the alliance to meet the challenges of the 21st century and to develop a site for a missile defense shield in Europe, a plan that angers Russia, which sits on the border of NATO's membership.

"I will continue to reach out to Russia. I sent Secretary Gates to Russia recently to have a full and transparent conversation with President Putin and his cabinet, to make sure that the Russians understand that this missile shield is not directed at them, but, in fact, directed at other nations that could conceivably affect the peace of Europe," Bush said.

Separately, Bush called Iraqi Prime Minister Nouri al-Maliki on Monday to mark the one-year anniversary of his inauguration.

Despite growing frustration in Congress with the al-Maliki government and a desire by Democrats and some Republicans to set benchmarks for progress there, Bush discussed political progress there and received an update on oil-sharing legislation and efforts to reform the country's constitution.

"The president reaffirmed his confidence in the prime minister and noted the courage that he has shown in a challenging and difficult year," Fratto said.

Fratto said it is hard to pin down when the Iraqi government will deliver on its promises of political reconciliation.

"Obviously we want the Iraqis and the Iraqi parliament to move as quickly as possible," Fratto said. "Progress on advancing these initiatives is not moving as quickly as anyone wants — and I think that includes Prime Minister Maliki and many members of parliament."

Fratto said the president would like a bill to come to him for funding U.S. troops in Iraq before Memorial Day, next Monday, and that is something leaders in Congress committed to do. He said evaluations of the troop build-up in Baghdad are premature as security operations there won't even be in place fully until mid-June.

Gen. David Petraeus, head of Multinational Force in Iraq, has said he plans to provide an assessment on that operation at some point in September. If operations are running on time, progress can be measured, but success on every other element in Iraq is dependent upon the security situation, Fratto said.

"You will not have political progress or economic reconstruction progress unless you have progress on the security front so we'll look forward to that," Fratto said.

FOX News' Bret Baier, Eve Zibel and The Associated Press contributed to this report.