WASHINGTON — The Bush administration is nearing the halfway point in its goal to admit 12,000 Iraqi refugees by the end of September, the State Department said Saturday amid a flurry of activity on the issue.

Several senators on Friday called for the appointment of White House coordinator for Iraqi refugees and said the administration had not done enough to help those who have fled Iraq. The next day, the department said it was on track to meet the 12,000 target.

Also Saturday, the U.S. diplomat dealing with the matter arrived in Jordan as part of a four-nation Middle East tour intended to help streamline the process, assess refugees' needs and determine how best they can be assisted.

The department normally releases refugee admission statistics on a monthly basis. But on Saturday, the department said that more than 1,000 Iraqis had been admitted to the United States in the first half of June.

The half-month figure for June is close to the 1,141 admitted for all of May, which was a record. May's admissions brought to 4,742 the number of Iraqi refugees accepted since the current budget year began on Oct. 1. With the latest report, that total is closing in on 6,000.

"We have thus far admitted over 5,800 refugees this fiscal year and have interviewed and conditionally approved more than enough to reach 12,000," said a department spokesman, Tom Casey. "While it will be a challenge, we are on track to meet our goal."

To meet its goal of admitting 12,000 by the end of the budget year on Sept. 30, the administration must allow in about 6,200 over the next 3 1/2 months.

The 12,000 target is still far lower than the number admitted by other countries and only a small slice of the some 2 million Iraqis who have fled to neighboring countries since the U.S.-led invasion in March 2003.

Sweden, for example, has granted asylum to about 40,000 since 2003.

Advocacy groups and lawmakers have criticized the U.S. for its poor performance on admitting Iraqi refugees.

The Mideast tour by James Foley, the department's senior coordinator for Iraqi refugees, will bring him to countries that have the largest populations of Iraqi refugees, including Turkey, Jordan and Lebanon.

He also planned a rare stop in Syria next week. Visits to Syria by U.S. officials are unusual due to strong U.S. objections to Syrian policies in Lebanon and its support for anti-Israel groups.

Foley's "visit to Syria is focused primarily on assessing the assistance needs of Iraqi refugees in that country and others in the region and looking at what additional steps the international community can take to address them," Casey said.

Some in Congress, however, think much more needs to be done.

On Friday, a group of lawmakers led by Senator Edward Kennedy, D-Mass., introduced a bill that would create an ambassador-level post at the White House to oversee efforts to assist Iraqi refugees. Currently, that policy is handled by the departments of State and Homeland Security.

"It's long past time for America to reaffirm our responsibility to end the refugee crisis caused by the Iraq war," said Kennedy spokesman Anthony Coley.