"I think it's important for the Government of Iraq. I think it's important for security and stability here," he added.
Meanwhile, President of the Kurdish Regional Government Massoud Barzani said that he would be happy to host US troops if the central government in Baghdad refuses to do so.
"The people of Kurdistan highly appreciate the sacrifices American forces have made for our freedom," Barzani said at a reception in Washington after meetings with President Bush and Secretary of State Condoleezza Rice.
Several Iraqi officials and analysts have said that they doubt that the Iraqi parliament will approve a deal before the end of the year, when a UN mandate governing US forces in Iraq expires.
White House spokeswoman Dana Perino said on Thursday: "I do think it will be hard for Iraq to pass it."
Without a new mandate, all US military activity in Iraq will have to cease or be in violation of international law. Troops could be confined to bases, and vital support operations for Iraqi forces -- training, transportation, communication, and air control -- would end.
"We have to have a legal framework to stay here," said General Odierno, who recently replaced General David H. Petraeus as commander of the 152,000 US troops in Iraq.
General Odierno said he sent Iraqi government ministers last week a detailed outline of the operational consequences of failure to obtain a bilateral agreement or an extension of the UN mandate.
US military projects that employ thousands of Iraqis would shut down; training of Iraqi forces would stop as would joint operations; air traffic control over Iraq would cease; border security would be Iraq's sole concern; and communications and logistics support for Iraqi security forces would end, he said.
The draft accord calls for US forces to leave Iraqi cities by June 30 and combat troops to exit by the end of 2011, unless requested to stay.