Mr Rumsfeld said the US was setting no penalties and holding the Iraqi government to no specific dates.
But he said the US had been working with the government of Iraqi Prime Minister Nuri Al-Maliki on a "way forward" that lays out a broad timetable projecting when certain tasks might be accomplished.
"For example, they have passed over two provinces to Iraqi governance. And they are planning to pass over the other 16," Mr Rumsfeld told reporters.
"And so the question is when do you think that might happen? When do you think the Iraqis might be ready to do that, to assume those responsibilities?" he said.
Mr Rumsfeld said the Iraqis have announced a reconciliation process, and so US Ambassador Zalmay Khalilzad and General George Casey, the US commander in Iraq, are "looking at that and saying when are the various elements of that likely to happen".
Mr Rumsfeld and other officials have said the discussions with the
Iraqis have been under way for several months.
But they appear to be taking on greater urgency in the face of escalating sectarian violence.
The US military said five more US troops were killed on Sunday, raising the toll of American military dead this month to 85, higher than in any single month since October 2005, when 96 US troops lost their lives.
Mr Rumsfeld said the violence followed a pattern in previous years of intensifying attacks during the Muslim holy month of Ramadan.
But other administration officials also have said insurgents appear to be stepping up attacks in hopes of influencing the US legislative and governor elections on November 7.
Amid an upsurge in violence there were concerns over the fate of a US soldier who had been reported missing in Baghdad. US and Iraqi forces were searching for him, the US military said in a statement.
Meanwhile Iraqi Deputy Prime Minister Barham Saleh had told British Prime Minister Tony Blair that half of Iraq's provinces would be under direct Iraqi control by the end of the year.
"By the end of this year, nearly seven or eight provinces of Iraq out of 18 provinces will be under direct Iraqi security control," he said, stressing the importance of Iraqis taking control with the backing of the international community.
"I do believe there is no option for the international community to cut and run -- the fate of Iraq is vital to the future of the Middle East and world order."
The meeting with Mr Blair at Downing Street came amid increasing debate over US and British strategy in Iraq, where violence is escalating.
Despite media reports in Britain Mr Blair's office denied there would be any talk of an exit strategy during his talks with Mr Saleh.
TV station raided
US troops have raided the offices of a television station affiliated with a key Shi'ite party in Prime Minister Maliki’s coalition government.
Al-Furat's deputy editor Haidar Kadhim said soldiers arrived at the station in central Baghdad last night and disarmed the guards.
He said the station remained on air and the soldiers left about two hours later after negotiations with party officials.