Most of the money will go to the army to pay for salaries and to fund the replacement or repair of equipment.
Congress has already approved $25bn in emergency funds for this tax year.
In a related development, a top US general has said the US army expects to keep about 120,000 troops in Iraq for at least two more years.
The number of US troops in Iraq rose to 150,000 last month in an effort to bolster security ahead of Iraq's election on Sunday.
The BBC's Nick Childs at the Pentagon says officials there are no longer making any secret of the fact that the original plans did not envisage having so many troops in Iraq at this stage.
In a statement, President George W Bush said he had pledged to give US troops "whatever they need to protect themselves and complete their mission".
The new money being sought would push war spending to almost $300bn since the 11 September 2001 attacks. That is in addition to the Pentagon's annual budget, which already totals more than $400bn.
Some of the $80bn will go to help pay for the training and equipping of Iraqi and Afghan forces and the construction of a new US embassy in the Iraqi capital, Baghdad, estimated to cost $1.5bn.
Spending request
Significant sums are likely to be allocated to help the new Palestinian and Ukrainian governments.
A senior administration official said the request "may be slightly above" $80bn.
On top of that, the package that Mr Bush will eventually put to Congress is also expected to include money for Asian nations hit by last month's tsunami.
In previous years, $120bn has been made available for Iraq and $60bn for Afghanistan.
The White House had not been expected to reveal details of spending request until after the release of the federal budget on 7 February.
But it decided to do so after congressional officials argued that withholding the costs from the budget would leave the administration open to criticism.
Democrats have accused Mr Bush of excluding Iraq-related costs from previous budgets to meet its goals of reducing its deficit, a charge which the administration denies.
The US is running a budget deficit of close to $500bn a year.