At the press conference, Bush was asked about his decision to commute the 30-month prison sentence of Lewis "Scooter" Libby, the former chief of staff to Dick Cheney, the vice-president.
Libby was convicted of lying and obstruction of justice in the investigation into the leaking of Plame's identity.
Sentence commuted
But 10 days ago, Bush labelled the sentence "excessive" and used his presidential powers to commute the sentence, though he left in place a $250,000 fine.
The president had initially said he would fire anyone in his administration found to have publicly disclosed the identity of Plame, whose husband, Joseph Wilson, was a vocal anti-war critic.
"It has been a tough issue for a lot of people in the White House, and it's run its course, and now we're going to move on," said Bush.
Meanwhile, also on Thursday, Reggie B Walton, the district judge who sentenced Libby, took issue with Bush's characterisation of Libby's sentence as "excessive", noting that the 2-1/2 year sentence was at the low end of federal sentencing guidelines.
"It is fair to say the court is somewhat perplexed as to how its sentence could be accurately described as 'excessive'", wrote Walton, who was appointed to his position by Bush.
Karl Rove, the White House political adviser, and Richard Armitage, the deputy secretary of state, were the primary sources for a 2003 newspaper article outing Plame.
Ari Fleischer, a former White House press secretary, also admitted telling reporters about her.
Jurors at the trial apparently believed prosecutors who said Libby discussed Plame with reporters from the New York Times and Time magazine. Libby was the only one charged in the matter.