BAGHDAD (Reuters) - Faced with a mounting military and civilian death toll and stiffening guerrilla resistance, President George W. Bush vowed on Monday that the United States would not run from its "vital" mission in Iraq.

Hours after Bush's pledge in a speech in Alabama, a U.S. soldier was killed and one wounded by a home-made bomb near Saddam Hussein's hometown of Tikrit, the U.S. military said.

This brought to at least 252 the number of U.S. soldiers killed by hostile fire since the U.S.-led invasion on March 20. The number of Iraqis killed is in the thousands and steadily climbing.

In Baghdad, an explosion echoed across the city after dark, followed by three mortar blasts near the headquarters of the U.S.-led administration in Iraq. U.S. officials said there were no reports of casualties.

The president's comments were his first since 16 American soldiers were killed when guerrillas shot down their CH-47 Chinook helicopter on Sunday in the worst single attack since the U.S. invasion.

"The enemy in Iraq believes America will run. That's why they're willing to kill innocent civilians, relief workers, coalition troops. America will never run," Bush said, despite falling approval ratings in the United States over the war.

"The mission in Iraq is vital," Bush added. But he did not refer to the downing of the helicopter or three other deaths which made Sunday the second worst day overall for the Americans of the conflict. At least 20 U.S. soldiers were wounded.

At least three people were killed when a bomb exploded on Monday outside a hotel used by Iranian pilgrims in the holy Shi'ite city of Kerbala, 90 km (56 miles) south of Baghdad, Shi'ite officials said.