Two more soldiers were killed last week in fighting west of Baghdad, the US military said on Tuesday.
Staff Sergeant George T Alexander Jr, 34, died on Saturday at Brooke Army Medical Centre in San Antonio, Texas, of wounds suffered on 17 October, when an explosive device detonated near his vehicle in the central Iraqi city of Samarra, the Defence Department said.
According to the Iraq Coalition Casualty Count website, there have been 2000 US deaths since US-led forces invaded Iraq in 2003, most killed in the uprising that gripped the country after Saddam Hussein was toppled.
However, the official Pentagon count, last updated on Tuesday, remained at 1993 military personnel killed and more than 15,000 injured since the start of the war.
"Two thousand is a significant number and will resonate with the US public," said Charles Heyman, a senior defence analyst at Jane's Information Group in London. "There is no doubt whatsoever about that.
"It will also resonate with the insurgents," he said.
Bush has warned the war in Iraq
will require more sacrifice
A Harris Interactive poll published on Tuesday in The Wall Street Journal found that for the first time, a majority of Americans (53%) believe the Iraq war was the "wrong thing to do".
Only hours before the number of US military fatalities in Iraq reached 2000, the poll showed that 44% said the situation for US troops in Iraq was getting worse, compared with 19% who thought it was improving.
The number of US dead is nevertheless dwarfed by the up to 30,000 Iraqi civilian casualties since US-led forces pushed across the borders in March 2003.
Between 26,690 and 30,051 Iraqi civilians have died since the invasion, according to Iraq Body Count which monitors press reports.
Growing discontent in the United States has put US President George Bush on the defensive.
On Tuesday, he warned the war in Iraq "will require more sacrifice" and ruled out any early withdrawal of US troops.
"This war will require more sacrifice, more time and more resolve," he said in remarks at Bolling Air Force Base. "The best way to honour the sacrifice of our fallen heroes is to complete the mission."
"In Iraq, there is no peace without victory. We will keep our nerve and we will win that victory"
US President George Bush
Early this month he rapped "self-defeating" commentators who had begun to suggest the US should withdraw its 140,000 troops.
"In Iraq, there is no peace without victory. We will keep our nerve and we will win that victory," Bush vowed.
White House press aides then choreographed a chat with US and Iraqi troops in Saddam's hometown of Tikrit, the high point coming when an Iraqi sergeant grabbed a microphone and gushed: "Thank you very much for everything. I like you!"
US Secretary of State Condoleezza Rice steadfastly refuses to say when troops might be pulled out, stressing they were in Iraq to wipe out the "malignant" influence of Islamic extremism in the Middle East.
Bush led the nation into war saying that Saddam had developed weapons of mass destruction and had links to al-Qaida, with the first claim having been proved false and the second remaining unproven.