WASHINGTON, March 11 – President Bush declared today that the United States was willing to train and provide military aid to "governments everywhere" in the fight against terrorism and for what he made clear would be battles beyond Afghanistan.

In a somber speech of war on the South Lawn of the White House that marked the sixth month since the Sept. 11 attacks, Mr. Bush significantly expanded the commitment of the United States to a global campaign against terrorism, saying that America would "actively prepare" other nations for the fight. Mr. Bush said for the first time that the United States would send 150 military trainers to the former Soviet Republic of Georgia, where he said terrorists working with Al Qaeda operate in the Pankisi Gorge near the Russian border.

"I have set a clear policy in the second stage of the war on terror: America encourages and expects governments everywhere to help remove the terrorist parasites that threaten their own countries and peace of the world," Mr. Bush said. "If governments need training, or resources to meet this committment, America will help."

The president's remarks were his most definitive description of the next phase in the campaign against terrorism and come at a time when Democrats have demanded a further explanation of the administration's goals.