But an opinion poll published the same day suggests his compatriots are losing faith in their president's policies on Iraq.
"The more successful we are on the ground, the more these killers will react. And our job is to find them and bring them to justice," Bush said.
"It's in the national interest of the United States that a peaceful Iraq emerge, and we will stay the course in order to achieve this objective," Bush added.
The president spoke as he welcomed his special envoy to Iraq, Paul Bremer, Defence Secretary Donald Rumsfeld, National Security Adviser Condoleezza Rice, the chairman of the joint chiefs of staff, General Richard Myers, and Central Command chief General John Abizaid for White House talks.
Meanwhile, Secretary of State Colin Powell appealed to the International Committee of the Red Cross and other agencies not to pull out of Iraq. He said their work was needed and their departure would be victory for "terrorists".
The bombings in the Iraqi capital killed 42 people and injured more than 200. The Red Cross headquarters was one of several buildings targeted in the nearly simultaneous attacks.
On Sunday, a US soldier was killed and 17 people, including 11 Americans, were injured in rocket attacks on Baghdad's al-Rashid Hotel, where US Deputy Defence Secretary Paul Wolfowitz was staying.
Colin Powell has urged charities
to stay in Iraq despite dangers
"Today was a difficult day and the last 24 hours have been very difficult," Powell said. "We're going ahead with our reconstruction plans and efforts."
All five bombings in Baghdad were human bomb attacks seemingly carried out by foreigners, US Brigadier General Mark Hertling claimed.
On top of the threat posed by loyalists of ousted President Saddam Hussein, the US-led occupation force has warned of the presence of foreign fighters, possibly linked to Saudi-born al-Qaida leader Usama bin Ladin or other Islamist groups.
However, the US has failed to provide any credible evidence that al-Qaida has been active in Iraq.
In a sign that the difficult situation in Iraq is taking a toll on Bush's popularity, half of respondents to a poll disapproved of the president's handling of the war. In late April, just 18% disapproved, according to the Gallup poll for USA Today and CNN.
Over the nearly six months since Bush declared an end to major hostilities, public support for the war dropped from 71% in late April to 54% now, said the pollsters on Monday.
Few members of Bush's own Republican party have withdrawn support for the war over that period, down from 90% in April to 88% now. Democrats show the largest drop, from 54% to 24%. Independents' approval slipped from 64% to 48%.
A growing number of respondents, 57%, said some or all US troops should come home. Two months ago, 46% said so.
As the 2004 presidential race gets off the starting blocks, 46% of registered voters would vote for Bush, while 43% said they would vote for an unnamed Democrat.