"We do believe that it is in the interest of the Iraqi government, it's in the interest of this country, and we have been and we will continue to support it and support its ratification," Barzani said.
Bush, who leaves office on January 20, discussed the agreement with Nuri al-Maliki, the Iraqi prime minister, on Monday.
The draft version has drawn criticism from Iraqi political figures on grounds that it undermines their war-torn country's sovereignty, likely to be a key theme in local and regional elections set for January 31.
Muqtada al-Sadr, the Shia leader, has said he opposes the pact, while Grand Ayatollah Ali Sistani, a senior Shia cleric, said in a statement from his office that any final deal must not harm Iraqi sovereignty.
The Iraqi cabinet on Tuesday authorised al-Maliki to negotiate changes in the pact, which will lay out the rights and responsibilities of US forces in Iraq beyond December 2008 when their present UN mandate expires.
Geoff Morrell, a spokesman at the Pentagon, said the proposed Iraqi amendments to the draft accord "are in the process of being translated and they will then be evaluated by our team. This process, I believe, will likely take several days."
"We want to be very deliberate about this, want to have a clear understanding of what precisely the changes they are looking to make entail," he said.
"It is our intention, certainly, to listen to them, to pay them proper respect."
Under the current proposal, US forces will withdraw from Iraqi cities by 2009 and from the whole country by 2011.
It also gives Iraq the power to prosecute US soldiers who are accused of committing serious crimes outside their bases and when off duty.
Mowaffak al-Rubaie, Iraq's national security adviser, and one of the negotiators, said the security deal would prevent the US military from launching attacks on Iraq's neighbours.
"There is a very clear article in the Sofa draft that says the US cannot, should not, launch any operation from Iraqi soil against other countries."
His comments followed the weekend raid by US troops on a village in northeast Syria which Damascus said killed eight civilians.
A US official on Monday said the incursion targeted a top Iraqi smuggler of foreign fighters who used the area just inside Syria to launch attacks.