The permanent Security Council members are now trying to cut the bill to $450 million or less, mainly by deploying fewer soldiers.
It will be formally presented on Tuesday to the three other permanent Security Council members, France, Russia and China, whose veto authority makes their votes crucial.
There is an unwritten rule that permanent Security Council members must vote for each other's candidacy on such groups.
At the same time, Russia, France and China, all permanent Security Council members, have been lobbying to remove economic sanctions on Iraq.
This was exactly the outcome that these three Western permanent Security Council members wanted, their diplomats say.
"There will be missions to the permanent Security Council members to reinforce efforts expended to reach an agreement on the implementation" of the cease-fire resolution, he said.
The American draft resolution is supported by the four other permanent Security Council members - Britain, France, the Soviet Union and China.
He also dismissed suggestions that Bonn would seek changes in the United Nations structure allowing it a permanent Security Council seat.
Leaving aside the United States, the four other permanent Security Council members - Britain, China, France and Russia - together pay 13.6 percent.