At a time when Iraqi insurgents are targeting local police officers and recruits for attack, the United States has raised by one-third -- to 135,000 -- the size of the Iraqi police force it says will be needed to help secure the country, according to information the administration has provided to Congress.

The challenges to the United States in training and deploying that many officers are considerable, officials acknowledge. Currently, about 82,051 Iraqi police officers are on the payroll, but only 32,880 have received training under U.S. guidance, according to figures provided by Capt. Steven Alvarez, an Army officer working with the Iraqi Interior Ministry. Of that number, Congress was told last week that only 8,200 had received the eight-week training; the rest got a more basic course for three weeks or less.

Deputy Secretary of State Richard L. Armitage described the latter group as "shake and bake" trainees, saying in congressional testimony last week that they were mostly former police officers under Saddam Hussein's government being trained "primarily in human rights, respect for law, things of that nature."

Although interim Iraqi Prime Minister Ayad Allawi and President Bush emphasized last week that progress is being made in training Iraqi police, others say the going has been slow.

A senior U.S. official in Iraq said in an interview last week that the new goal for 135,000 officers may not be reached for two more years under the best of circumstances. Officials point, among other things, to a lack of qualified personnel and appropriate training facilities.

More than 750 Iraqi police officers and hundreds more recruits have been killed over the past 10 months, said the senior official, who would speak only on the condition of anonymity. At the same time, officials in Baghdad said such attacks on recruits haven't stemmed the flow of willing volunteers.

The Iraqi Police Service is only one of several security forces that Americans are working to train and equip. Officials say this is essential to quell the insurgency, provide security for Iraq's January election and set the stage for U.S. forces to diminish their role in the country.

In addition to the national police force, the security array includes military units such as the Iraqi army, the Iraqi National Guard, the Iraqi Prevention Force and Iraqi Special Operations Forces, and police-type units such as the Department of Border Enforcement and the Facilities Protection Service, whose members guard government buildings.

Estimates of the number of Iraqi police officers have varied, and officials say record-keeping is primitive and chaotic.

"The payrolls are stubby pencil right now," said the U.S. official in Baghdad. He described a system in which a handwritten list of police to be paid is generated in towns and cities across Iraq, approved at a regional level and then delivered to Baghdad, where cash is taken from the Finance Ministry and sent back down the line. "It is all cash right now," he said. The Iraqi Interior Ministry is "determined to set standards and have a database of those who are on the payroll."

To help solve the Interior Ministry's problems in managing the force, U.S. officials have introduced a new high-tech system in which digital fingerprints and retinal eye scans are taken of individuals on the force. To that they are adding the individual's educational and employment background to help them decide whom to keep on, whom to retire and whom to hire.

Anthony H. Cordesman, senior fellow at the Center for Strategic and International Studies, released a study Friday showing that the Iraqi Police Service payroll list "includes large numbers of pensions and 'non-performing' police" known not to be serving. He also said the overall police numbers were dropping "in part because of desertions and purging of low-grade personnel."

Lt. Gen. David H. Petraeus, who has taken charge of all Iraqi security training, has tried to purge the rolls of unqualified or unfit officers even as he works to recruit and train new ones. In June he received $20 million in Iraqi oil money to provide severance pay. At that time, 120,000 people were on the police payroll, but the force was authorized to have only 90,000.

Another new problem for Petraeus is what to do for the families of police who are killed by insurgents and for those officers who have been wounded and are now disabled. The Petraeus fund has grown to $60 million, the official said, in part to address these new problems.

And officials had hoped that a facility in Amman, Jordan, would be able to train 3,000 Iraqis at a time in an eight-week program, but it has not performed at that pace. A new facility is planned for Baghdad and other locations across the country.

Petraeus, in an op-ed column Sunday in The Washington Post, said progress was being made.

"In the past week alone, some 1,100 graduated from the basic policing course and five specialty courses. By early spring, nine academies in Iraq and one in Jordan will be graduating a total of 5,000 police each month from the eight-week course, which stresses patrolling and investigative skills, substantive and procedural legal knowledge, and proper use of force and weaponry, as well as pride in the profession and adherence to the police code of conduct."

Finding people to conduct the training continues to be a challenge, though. Officials said last week that they have filled their needs for about 500 foreign trainers, but the Justice Department's International Criminal Investigation Training Assistance Program was still advertising for instructors to sign on for six-month or year-long tours in Iraq.

The pay: an annual rate of $153,000, almost all tax-free, plus room, board, travel expenses and paid vacations, available to U.S. police officers with five years of experience, even if they had no prior training duties.