Wrangling over the draft Sofa had become increasingly fraught in recent weeks as the expiration of the UN mandate in December nears.
The issue of immunity for US troops and Iraqi jurisdiction over their actions has been the main point of contention between the US and Iraqi governments.
Susan Ziadeh, US embassy spokeswoman, said on Thursday that the revised draft was an attempt by Washington to secure a lasting agreement on the presence of US forces in Iraq.
"We've responded positively in order to move this process forward in a way that reflects the sovereignty of both sides," she said.
Ali al-Dabbagh, a spokesman for the Iraqi government, told state television on Thursday that Washington had made some of its own changes to the Sofa draft, in response to Baghdad’s demands.
"These modifications now need a meeting with the American side to reach a joint understanding," Dabbagh said.
"The atmosphere is positive; the Iraqi side needs more time to give the main political entities time to review the proposed US remarks and modifications," he said.
However, al-Hurra, a television channel financed by the US, said that Washington has responded only to some of the changes Baghdad wants.
The draft deal is already over three months past its deadline, with Iraq looking for greater powers over American troops and civilians.
Iraq reportedly wants to be able to prosecute them for crimes committed on their bases, in addition to crimes committed outside their bases while off duty.
The latest draft of the agreement stipulates that US forces will withdraw from Iraqi cities by June 2009 and leave the country by 2011.
Should there be a failure to reach a deal, a request for a new UN mandate will need to be submitted to the world body’s Security Council.