Al-Dabbagh said his remarks constituted the government response, but it had not been officially conveyed to the Americans. There was no immediate comment from U.S. officials, who had described the latest draft submitted to the Iraqis as a "final text."
Privately, however, some U.S. officials have said they expect protracted haggling over the agreement, with the Iraqis pressing for more concessions until the last minute.
"The American answer is not enough for the government to accept it in its current form," al-Dabbagh told The Associated Press. "There are still some points in which we have not reached a bilateral understanding."
Al-Dabbagh said the government was inviting the U.S. "to give answers that are suitable to the Iraqis."
The agreement must be approved by parliament before the Dec. 31 expiration of the U.N. mandate that allows U.S. troops to operate legally. Without an agreement or a new U.N. mandate, U.S. military operations would have to stop as of Jan. 1.
Al-Dabbagh did not spell out in detail what points the Iraqis still find unacceptable, but they probably include Baghdad's demand for expanded legal jurisdiction over U.S. soldiers.
The current draft allows Iraqi courts to prosecute soldiers accused of major, premeditated crimes allegedly committed off post and off duty. The Iraqis had asked for elaboration on those charges and a greater role in determining whether specific cases met the criteria for trial in their courts.
But the agreement faces strong opposition, especially within the majority Shiite community which is the base of Prime Minister Nouri al-Maliki's political support.
Several influential Shiite clerics have spoken out against the deal, and radical cleric Muqtada al-Sadr has vowed to oppose it.
In addition, the Sunni vice president, Tariq al-Hashemi, has called for a national referendum - a move that would effectively kill the deal because it would be impossible to arrange a vote before the mandate expires.
Iraq's neighbors Syria and Iran have urged the Iraqis to reject the deal.
Among other things, the latest U.S. proposals remove language authorizing Iraq to ask U.S. soldiers to stay beyond 2011 and ban cross-border attacks from Iraqi soil, according to a copy of the draft obtained Monday by The Associated Press.
The latest U.S. draft also strengthens language regarding Iraqi sovereignty but does not appear to make significant changes in the limited legal authority granted to Iraq to prosecute U.S. soldiers.
Al-Maliki plans to show the draft to President Jalal Talabani and the two vice presidents shortly. Later, he will submit it to the Cabinet and if the ministers agree, he will forward it to parliament for a final decision.
However, al-Dabbagh's comments indicate that al-Maliki is not ready to ask for Cabinet approval.
The latest draft states that U.S. troops must vacate Iraqi cities by June 30, 2009 and leave the country entirely by Dec. 31, 2011. The previous draft authorized the Iraqi government to ask U.S. troops to stay beyond that for training and other assistance.
But the current draft states simply that "United States forces shall withdraw from all Iraqi territory no later than Dec. 31, 2011."
The draft also recognizes the right of each country to remove U.S. troops before that deadline.
It also returns control of airspace to the Iraqis but provides that the government may ask the U.S. to provide "temporary support" in surveillance and air control.
The draft also gives Iraq the right to inspect and verify names of all U.S. service members and contractors entering and leaving the country and provides for the U.S. to take "appropriate measures" to deal with any threat to Iraq or its "democratic system and elected institutions."
President-elect Barack Obama pledged during the campaign to bring all combat troops home within 16 months of his inauguration Jan. 20. An Iraqi official said Obama had been briefed on the current draft.
The official spoke on condition of anonymity because the information is sensitive.
The draft agreement - 24 pages in the English version - also states that "Iraqi land, sea and air shall not be used as a launching or transit point for attacks against other countries."
Iraq insisted on the addition after last month's U.S. raid into neighboring Syria and in a bid to ease fears in Iran, which strongly opposes the deal.
As a further assurance, the deal is now officially an agreement "on the withdrawal of United States forces from Iraq" and the "organization of their activities during their temporary presence."
The deal had been envisioned as establishing a long-term security relationship when it was first discussed between al-Maliki and President Bush last year.