If finalized, the approval would allow the Gulf island to purchase 19 of the jets from Maryland-based Lockheed Martin Corp., plus improvements to other jets in Bahrain's fleet.
Though Congress has opportunities to block the sale, it is unlikely it will act to do so, given the Republican majority's strong support for the sale.
The decision is the latest signal that the Trump administration is prioritizing support for Sunni-led countries seen as critical to opposing Iran's influence in the Mideast over human rights issues that Obama had elevated.
Under Obama, the United States withdrew approval before the fighter jet deal was finalized because it said Bahrain hadn't taken steps it had promised to improve human rights.
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Senate Foreign Relations Committee Chairman Bob Corker's office said the committee was told yesterday by the State Department that it plans to proceed with the sale. The State Department declined to comment.
Then the State Department will send a formal notification to Congress, setting off a final, 30-day review period, during which Congress could pass a joint resolution or take other steps to stop the sale.
Lockheed had lobbied strenuously for the sale's approval, even as rights groups and pro-democracy activists urged the administration not to jettison human rights conditions.
Brian Dooley of the Washington-based group Human Rights First said decoupling the sale from such conditions would "encourage further repression" and fuel instability during a tense period for Bahrain.
But Corker, a Republican from Tennessee, praised the move and said the caveats would have been "unprecedented and counterproductive" for security and human rights.
"There are more effective ways to seek changes in partner policies than publicly conditioning weapons transfers in this manner," Corker said in a statement.