"I have given it my all, sir, and I have given you my all, sir," McClellan responded.
McClellan, who was named as press secretary shortly after the 2003 US-led invasion of Iraq, has been in the job for more than two and a half years and became one of the most visible faces of the Bush administration.
Meanwhile Karl Rove, one of the US president's most trusted political advisers, is reportedly giving up his policy role to focus on politics ahead of the US midterm elections, administration officials said.
Rove has been deputy White House chief of staff for policy development and Bush's top political adviser.
On Tuesday, Bush also nominated Rob Portman, the trade representative, as the White House budget director.
Bush selected Susan Schwab, the deputy trade representative, to move up as Portman's replacement.
Many of the recent changes stem from Bush's appointment last week of new White House chief of staff Joshua Bolten.
The latest flurry of job moves comes as part of efforts to re-energise the Bush administration which has been hit by record-low opinion poll approval ratings for the US president.