President Bush has approved adding 4,400 more U.S. troops to a force buildup already ordered to try to bring security to Iraq, the White House said today. Bush formally requested about $3.2 billion to pay for the additional deployment, even as he and Democratic lawmakers battle over his Iraq strategy.In January, Bush said he would deploy 21,500 more U.S. troops to Iraq to try to stabilize Baghdad and restive Anbar province. The new U.S. military commander in Iraq, Gen. David Petraeus, has since said more troops will be needed in support of that troop buildup. Gordon Johndroe, spokesman for the White House National Security Council, said the extra troops would include up to 2,400 military police to handle an anticipated increase in Iraqi detainees.