Two rockets, on crude self-timers, were aimed at the operating base of British troops in mountains near Gardez, in the Paktia province.
The attempt was foiled after a local warlord, Sherzaz, discovered the 107mm rockets 7km (4 miles) southeast of the marines' base and informed British troops.
It is not known who planted them.
Marines say it is possible it was al-Qaeda or Taleban fighters still left in the area and not found by Operation Snipe.
Warlord's alert
Marine Lieutenant Colonel Ben Curry said the warlord's motives for informing the Marines about the rockets are unclear.
He could have had a genuine concern for the welfare of the British commandos or might have been trying to curry favour, he said.
It is the first time during Operation Snipe that British forces have been aware of being targeted.
British commanders say the rockets were not accurately aimed and may not have hit the marines' position if fired, but they described the discovery as significant.
Lieutenant Colonel Curry said the rockets were wired to a timer to allow the assailants to escape before they exploded.
"[The timer] was dripping. It's a serious incident," he said.
"I'm not saying they would have actually landed on the forward operating base because it's a fairly inaccurate weapons system."
The operating base is the centre for re-supplying the troops in the mountains and refuelling the helicopters which carry them.
It is also a staging post for the marines and some were passing through the position on their way back to the headquarters in Bagram.
The news comes within days of the marines destroying an enormous ammunition store containing tens of thousands of rockets, found in several caves near a main road between the cities of Khost and Gardez.