The covert nature of President Barack Obama’s plan to arm Syria’s rebels has left Congress’ intelligence committees with what amounts to sole jurisdiction over the latest phase of U.S. intervention in the Syrian civil war.

But unlike the Senate Foreign Relations Committee, which voted on a bipartisan basis to arm the opposition in May, and the Armed Services Committee, whose chairman wants the administration to consider air strikes in Syria, Senate Intelligence Committee members are not at all comfortable with plans to send arms to opposition fighters.

“The Intelligence Committee members, not unanimously but an overwhelming majority on both sides, have a lot of concerns with giving aid to the Syrian rebels,” said one aide to a senator on the panel. “Their big concern is that you’re actually giving … weapons systems to people that could potentially fall into the hands of al Nusra,” the aide said, referring to the jihadi organization that is among the patchwork of rebel groups fighting to unseat longtime President Bashar al-Assad.

The committee’s chairwoman, Sen. Dianne Feinstein, D-Calif., was tight-lipped Wednesday on Syria, declining to comment on recent reports by The Associated Press and Reuters that her panel and her counterparts in the House have holds on the money the White House is seeking to pay for the arms.

“Obviously one always has concerns” about programs like this, Feinstein said, “but I think those concerns are being met.” Asked whether they were being met by the Obama administration, specifically, Feinstein nodded.

Intelligence Committee members’ reticence on arming rebels contrasts sharply with another key Senate panel, Foreign Relations, whose members backed legislation (S 960) authorizing the supply of small arms to vetted moderate opposition groups on a strong bipartisan vote, 15-3.

But because the White House has chosen to keep the program classified — it won’t even confirm publicly that it is preparing to send arms to the opposition — and wants to pay for the arms transfers via the intelligence budget, the Foreign Relations Committee has largely been sidelined from the latest round of debate. Members of the panel say they have been briefed as a group and as individuals on Syria — by Secretary of State John Kerry, among others — but they haven’t gotten the same level of detail on the arms program as their colleagues on the Intelligence Committee.

The same goes for the Senate Armed Services Committee, although Chairman Carl Levin, D-Mich., said Tuesday there are plans for a closed committee hearing with administration officials next week on Syria.

Levin and independent freshman Sen. Angus King of Maine, who sits on both the Armed Services and Intelligence committees, issued a statement Tuesday calling on the Obama administration to convene a meeting of officials from 11 countries that support the Syrian rebels to plan additional steps that could be taken to escalate military pressure on the regime of Assad. The two senators just returned from a trip to Turkey and Jordan to discuss the ongoing conflict in Syria, which has now killed more than 100,000 people since it began nearly two and a half years ago.

Perhaps most critically, neither Foreign Relations nor Armed Services has leverage over the funding of arms transfers to Syrian rebels, because the money is not coming from parts of the budget they oversee.

Senate Foreign Relations ranking Republican Bob Corker of Tennessee complained Tuesday that the White House’s covert approach on Syria “undermines our foreign policy efforts.”

“What ends up happening is you never make a public case for our public policy,” he said. “And, candidly, in the process Congress avoids having any ownership of it.

“It puts the Intelligence Committee in a very awkward place,” he added, because “all of a sudden if they approve something like this, they own it.”

While he emphasized that he supports the policy to arm vetted opposition groups — he was a co-sponsor of the Foreign Relations Committee legislation — Corker said he was “glad the administration has gotten push-back by trying to do this covertly. They should come and talk about this openly and we as a Congress should approve this openly.”

Jonathan Broder contributed to this report.