By Judy Aita
Washington File United Nations Correspondent

New York -- Terrorists holding American hostages will not shake the determination of the United States to stay the course in Iraq, President Bush said September 21. "America has given its word to help and we'll keep our word."

Speaking to reporters after a private meeting with Iraqi Interim Prime Minister Iyad Allawi, Bush spoke of Americans Eugene Armstrong and Jack Hensley, who were beheaded by terrorists. "These killers want to shake our will. They want to determine the fate of the Iraqi people. We will not allow these thugs and terrorists to decide your fate and to decide our fate."

Allawi said that "the war now in Iraq is really not only an Iraqi war; it's a war for the civilized world to fight terrorists and terrorism."

"There is no route but the route of winning, and we are going to prevail, and we are going to win, regardless of how much damage they are going to make and cause in Iraq and elsewhere," the prime minister said. "They want to undermine us in Iraq and to move from Iraq to undermine the region."

"[I]t's very important for the people of the world really to know that we are winning, we are making progress in Iraq," he said.

"Najaf, Samarra, Mosul, Basra are all live examples that a lot of progress has been made," Allawi said. "Unfortunately, the media have not been covering these significant gains in Iraq."

Progress has been made "because of the determination of the Iraqi people, the light that they are seeing at the end -- democracy will prevail, the rule of law will prevail, the issues and culture of human rights will prevail," the prime minister said.

Allawi will address the United Nations and the U.S. Congress during his stay in the United States.

Bush agreed that Allawi's visit to the United States was important because "the prime minister will be able to explain clearly to the American people that not only is progress being made, that we will succeed."

"The American people have seen horrible scenes on our TV screens, and the prime minister will be able to say to them that in spite of the sacrifices being made, in spite of the fact that Iraqis are dying and U.S. troops are dying as well, that there is a will amongst the Iraqi people to succeed."

Bush said that he is confident that "Iraq will be a free nation, and as a free nation, our world will be safer and American more secure."

Bush and Allawi held a private meeting while were attending the opening of the 59th session of the U.N. General Assembly.

In his address to the assembly, Bush urged nations to respond to the prime minister's request and do more to help Iraq face increased terrorist attacks, hold elections, restore the economy and establish democracy.

The United States "will stand with the people of Iraq until their hopes of freedom and security are fulfilled," Bush told the assembly.