The numbers suggest that while the air strikes have not deterred foreigners, they have also not incited larger numbers to counter the American-led campaign, the paper said, quoting US intelligence and counterterrorism officials.
"The flow of fighters making their way to Syria remains constant, so the overall number continues to rise," a US intelligence official said.
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But it could be weeks before a change in the rate becomes apparent, because of a lag in the intelligence that the CIA is examining, the Post quoted US officials as saying.
It said the trend over the past year suggests there are more than 16,000 foreign fighters in Syria, the Post said.
Reasons for the flow include sophisticated recruiting campaigns by radical groups in Syria like the IS jihadists and the relative ease with which people can travel to the country from North Africa, the Middle East and Europe.