Mr Bush described the bombers as "radical killers" who had no respect for individual life.
The US president also expressed his sympathy for the victims and their families, and he warned that America would not be intimidated by the attack, which Pakistani officials blamed on a suicide bomber.
"We will continue to hunt them down and seek justice," he said.
The US has now closed its diplomatic missions in Pakistan as well as the American Center in Islamabad. It is not clear when they will re-open.
A previously unknown group called "al-Qanoon" claimed responsibility for the attack in a handwritten statement delivered to media offices in Karachi.
"America, its allies and its slave Pakistani rulers should be prepared for more attacks. The bomb blast is the beginning of al-Qanoon's jihad activities in Pakistan," the statement said.
Regional police chief Syed Kamal Shah said that while he had not heard of the al-Qanoon organisation, he was still taking the letter seriously and would investigate the claim.
Forceful blast
White House spokesman Ari Fleischer also condemned the attack, describing it as a "vivid reminder" of the dangers Americans face in the war on terror.
"It's also a reminder of the risk that men and women in the foreign service take every day in doing their jobs," he said.
No foreigners or staff at the consulate were killed in the blast but one US Marine and five Pakistani employees are reported to be among the wounded.
Four Pakistani policemen guarding the heavily-fortified building were among the dead.
The explosion, which blew a gaping hole in the mission's perimeter wall, was the second in Karachi in a matter of weeks.
It comes a day after US Defence Secretary Donald Rumsfeld had talks in Islamabad with Pakistan's President Pervez Musharraf on curbing extremism in the region.
India 'not ruled out'
Pakistan's information minister said the involvement of the Indian intelligence services could not be ruled out.
India has condemned the attack.
Police said the bomb was concealed in a white vehicle that the driver crashed into a police kiosk at the southern end of the consulate.
It left a crater about 1.5 metres (five feet) deep, and a hole about three metres (10 feet) wide in the perimeter wall.
"There was smoke everywhere... moments later, I saw a man's body flying in the air, and he fell near me. He was badly injured. Before we could give him water or medical help, he died. It was a horrifying scene," eyewitness Sharif Ajnabi told the Associated Press.
Terrified guests at the next-door Marriott luxury hotel were reported to have packed bags and rushed to check out within minutes of the bombing.
Security in the area around the consulate is very high - no cars have been allowed to park nearby since an attack in Karachi last month, although they can still drive down the street.
Al-Qaeda 'link'
A bomb attack outside Karachi's Sheraton hotel on 8 May killed 11 French nationals and three Pakistanis.
Pakistani police suspect that attack was the work of Osama Bin Laden's al-Qaeda network.
Many al-Qaeda members are believed to have fled into Pakistan after the defeat of the Taleban in neighbouring Afghanistan.
In March, a grenade attack on a church in Islamabad left five people dead, including two Americans.
Many foreign diplomatic staff have left Pakistan following the attacks.
Last January General Musharraf made a televised speech to the nation in which he pledged to eradicate extremism in Pakistan.
But critics say he has made little headway in fulfilling his promise.