BAGHDAD, May 3 (Reuters) - Syria is doing more to stop the flow of foreign fighters coming across its border into Iraq, the U.S. military said on Thursday.

U.S. military spokesman Major-General William Caldwell said insurgents were still crossing the border into Iraq's vast western desert, where Sunni Islamist al Qaeda in Iraq has influence, but numbers were slowing. "There has been some movement by the Syrians ... there has been a reduction in the foreign fighter flow making their way into Iraq, as we have observed here over the last month," Caldwell told a news conference.

The United States has accused Syria of not doing enough to stop the flow of foreign fighters coming into Iraq. Caldwell did not give precise details on what Syria was doing to stem the flow.

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