The Pentagon says its bombing campaign has significantly weakened Baghdad's defences, while President George W Bush has said the war will not end until the Iraqi people are free.
Bush: 'Coming with a mighty force'
A Pentagon spokeswoman also said members of Saddam Hussein's family were trying to flee Iraq on a day of bullish statements from Washington.
Mr Bush promised the Iraqi people that "we are coming with a mighty force to end the reign of your oppressors.
"We will not stop, we will not relent until your country is free," he said in a speech to US Coast Guard officers and enlisted personnel in Philadelphia, Pennsylvania, on Monday.
At a Pentagon briefing, Major General Stanley McChrystal said US and UK forces dropped 3,000 bombs over the weekend - more than a third of the total to date in the 12-day war.
He said the intense air campaign had forced Iraq to redeploy Republican Guard troops to shore up defences.
The claim about members of Saddam Hussein's inner circle attempting to leave Baghdad came from Pentagon spokeswoman Victoria Clarke.
"We have seen some reports recently [...] that some family members, including family members of very senior officials, are trying to get out of the country," she said at the briefing.
She would not say where the reports came from, other than to specify that they were not from the press.
On the diplomatic front, US Secretary of State Colin Powell is to travel to Brussels and Ankara this week following disputes with Turkey and some leading European Union countries in the run-up to the war.
He will meet Turkish officials on Wednesday to discuss the establishment of a "representative government" in Iraq, State Department spokesman Richard Boucher said.
In Brussels on Thursday he will hold talks with both Nato and European Union leaders about the reconstruction of Iraq.
Turkey refused to let the US launch an invasion of Iraq from its territory, although it has allowed Washington to use its airspace.
Mr Powell told reporters that part of the purpose of his visit was "to make sure that we have a common understanding of the situation in northern Iraq".
There have been concerns that Turkey will send troops into Kurdish-controlled northern Iraq in order to keep its own restive Kurdish population under control.
France and Germany opposed US and UK efforts to secure UN Security Council backing for the war.