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The Houthis have been conducting near daily attacks on commercial and military ships in the Red Sea and Gulf of Aden, launching drones and missiles from rebel-held areas of Yemen. The attacks -- which are often unsuccessful but at times have struck the ships — have disrupted a crucial shipping route.

In response, the U.S. and allies have been forced to increase their military ship presence along the waterway, and on several occasions have launched wider retaliatory strikes on ammunition, weapons and other facilities. U.S. ships and fighter jets have also been routinely bombing Houthi drones and missiles that are in place and preparing to launch.

Grynkewich said it's difficult to know exactly how much the Houthis' weapons supplies have been eroded by the U.S. strikes, because officials didn't have a detailed intelligence assessment of their capabilities before the attacks began.

“The challenge for us is understanding what the denominator was at the beginning. In other words, what did they have on hand to start with? We obviously know how much we have struck and we have assessments of how successful those strikes were.� he said. “ The other complicating factor is Iranian resupply.�

He said the U.S. believes the Houthis had dozens of anti-ship ballistic missiles when they started, and they've launched dozens. So understanding how much Iran is able to restock the group is key.

The Houthis have defended their campaign as an effort to pressure in the Gaza Strip. The ships they've targeted, however, have largely had little or no connection to Israel, the U.S. or other nations involved in the war.

Speaking to reporters, Grynkewich said the Houthis are more independent and more difficult for Iran to control than other Tehran-backed militias in Iraq and Syria. Those groups have largely paused their attacks on U.S. forces at based in Iraq and Syria since early February, when the U.S. launched a massive retaliatory assault against the groups and sites connected to Iran's Revolutionary Guard.

U.S. officials have said they believe pressure from Iran was part of the reason for the pause. But Grynkewich said the Houthis are “not quite as responsive� to Iranian direction.

He said that even if Iran tried to crack down on the Houthis or cut off weapons or other supplies, it would take time for that to have an effect.