WASHINGTON—The Bush administration said Tuesday it could admit almost 8,000 more Iraqi refugees to the U.S., putting it within reach its goal of admitting 12,000 by the end of September.

After months of falling short of the average number of admissions needed to meet the target, officials said 1,141 Iraqi refugees had been admitted in May, the first time since 2003 that the 1,000 per month mark has been surpassed. Officials also for the first time released figures for Iraqi refugees in the processing pipeline who have not yet been allowed in.

The 12,000 target is still far lower than other many countries, notably Sweden, which has admitted about 40,000 since 2003, and only a small slice of the some 2 million Iraqis who have fled to neighboring countries, mainly Syria, Jordan, Turkey, Lebanon and Egypt. About 17,000 of those Iraqis have been referred to the United States for resettlement by the United Nations this year.

The United States has come under criticism from advocacy groups and lawmakers for its poor performance on admitting Iraqi refugees who have fled violence since the 2003 U.S.-led invasion. Many critics say, and officials acknowledge, that the administration has a moral obligation to the refugees and is not doing enough to help them.

With time running out to meet this year’s U.S. goal, officials acknowledged that they still face an uphill struggle to hit the target, but they said they were encouraged by the May arrivals and confident that that figure would rise, possibly to more than 2,000, in each of the next four months, making up for past shortfalls.

“We have a long way to go and we recognize that,” said James Foley, the State Department’s coordinator for Iraqi refugees. Foley was appointed by Secretary of State Condoleezza Rice to streamline the admissions process and meet the goal of admitting 12,000 Iraqi refugees during the current budget year.

“It’s a tall order,” he said. “It’s a difficult hurdle, but we are determined to succeed and we are increasingly confident that we can. The infrastructure is now fully in place.” May’s admissions bring to 4,742 the number of Iraqi refugees allowed into the country since the budget year began Oct. 1, 2007. To meet its self-imposed target, the administration must allow in another 7,258 by the end of the budget year, or 1,815 a month, on Sept. 30. Foley said there are now about 7,800 would-be Iraqi refugees who have either been fully or conditionally approved by Homeland Security Department interviewers for resettlement in the U.S. and could arrive in the coming months.