Bush said the goal of the US mission in Iraq was not to eliminate such attacks but to engage in a long-term effort to enable a democracy that can function despite continuing violence.
"Americans have got to understand it takes a while to mobilise additional troops and move them from the United States to Iraq," he said.
"It's a well-conceived plan by smart military people, and we owe them the time and we owe them the support they need to succeed."
Bush's plea came as two Republican senators broke ranks with calls on Wednesday for changes in US strategy.
Senator Richard Lugar warned that the so-called "surge" of troops would not work, while Senate Republican George Voinovich, who like Lugar has resisted Democratic attempts to curtail Bush's war powers, recommended a disengagement from Iraq.
"Even as our troops are showing some success in cornering and trapping al-Qaeda, they face a lot of challenges"
But Bush noted that the last of the reinforcements arrived in Iraq only earlier in June – scarcely enough time to assess the success of the new troop infusion.
"Right now, we're at the beginning stage of the offensive. We finally got the troops there," he said.
The US president ordered 21,500 additional combat troops to Iraq in January.
"Even as our troops are showing some success in cornering and trapping al-Qaeda, they face a lot of challenges," Bush said.
The US military reported that two recent roadside bombs in Baghdad have taken its military losses to 77 in June and 3,554 since the March 2003 US-led invasion, according to an AFP count based on Pentagon figures.