US officials said the extra troops would be sent from other areas of Iraq.
An average of more than 100 civilians per day were killed in violence in Iraq in May and June, according to a report by the UN Assistance Mission in Iraq.
White House spokesman Tony Snow admitted that a plan brought in six weeks ago to improve security in the Iraqi capital “has not achieved its objectives”.
“It’s pretty clear that there’s an attempt in Baghdad to create as much chaos and havoc as possible,” he said, quoted by AP news agency.
“And it’s important to make sure that we address this.”
When the two leaders met in Baghdad last month, President Bush offered support to a newly-formed government which had just been boosted by the killing of the insurgent leader Abu Musab al-Zarqawi.
The mood then was unusually positive, reports the BBC’s James Coomarasamy in Washington – but this latest meeting comes on the back of a failed security operation in Baghdad.
Mr Maliki has also pledged to convey his concerns about Israel’s actions in Lebanon, arguing that images of suffering Lebanese civilians are a powerful recruiting tool for extremists.