US Secretary of State Colin Powell believes there is a strong chance of securing nine or 10 votes for the amended draft resolution on Iraq.
But he was less certain about its chances of being adopted by the Security Council.
"It's not clear yet. We will have to wait and see when the vote is taken sometime this week but I am encouraged by the discussions I have been having with a number of members of the Council," Mr Powell told NBC.
"I think we have a chance to get, a strong chance ... that we might get the nine or 10 votes needed for passage of the resolution and we'll see if somebody wants to veto it," he added.
Mr Powell said if Saddam did not agree to give up his weapons of mass destruction - something he said he did not expect - then "the probability of war is rapidly increasing".