The CIA could begin shipping arms to Syria in the coming weeks, after two US congressional panels cleared the way for the controversial transfer of weapons.

The White House announced in June that it would provide limited military support for vetted rebel groups, which have recently been struggling in their campaign against President Bashar al-Assad.

Republicans and Democrats on the House and Senate intelligence committees have expressed concerns that arms could end up in the hands of Islamist militants fighting in the region – or not do enough to tip the balance in the civil war.

Mike Rogers, chairman of the House committee, said on Tuesday that the panel had agreed to support the plan to arm the opposition fighters. However, the committee made clear it has only agreed reluctantly and retained serious anxieties about whether Barack Obama's new policy would work.

"The House intelligence committee has very strong concerns about the strength of the administration's plans in Syria and its chances for success," he said in a statement, after Reuters reported the decision. "After much discussion and review, we got a consensus that we could move forward with what the administration's plans and intentions are in Syria consistent with committee reservations."

Representative Adam Schiff, a Democrat among the minority on the House committee who opposes sending arms, said: "It's too late to affect the outcome with a small amount of arms."

The Senate committee decided earlier this month that it would back the plan to back the rebels, on the condition they received updates on the covert programme. Both committees have been meeting behind closed doors to discuss Obama's desire to transfer light weapons and ammunition to rebel insurgent organisations, as well as to supply some training.

The timeline for the weapons transfer is unclear, but reports suggest the process could take place over the next several weeks. Syrian opposition groups have said publicly they hope they will begin receiving the deliveries in August.

US secretary of state John Kerry and other senior officials in the administration have been lobbying hard behind the scenes to persuade Congress to back the new policy.

Obama, who has been reluctant to engage too deeply in the Syrian conflict, changed its position on arming opponents of Assad's regime last month, after concluding Syrian forces had used chemical weapons against civilians. The White House described that development as Assad crossing a "red line".

For now, a limited policy of supplying small arms to rebel groups appears to be as far as the Obama administration will go.

The top US military officer warned senators on Monday that taking military action to stop the bloodshed in Syria was likely to escalate quickly and result in "unintended consequences". Alluding to the occupations of Iraq and Afghanistan, General Martin Dempsey, chairman of the joint chiefs of staff, said that once the US became embroiled militarily in the Syrian civil war, "deeper involvement is hard to avoid".

He said: "We have learned from the past 10 years, however, that it is not enough to simply alter the balance of military power without careful consideration of what is necessary in order to preserve a functioning state."