Military top brass said yesterday that soldiers were conducting offensives "in some forest locations" in the area after it was announced last week that operations were imminent.
The Sambisa Forest is located in the state of Borno, some 80 kilometres (50 miles) from the town of Chibok, from where more than 200 schoolgirls were kidnapped in April last year.
It has been claimed the 219 schoolgirls still being held were initially kept in the former game reserve, although others have said they may have been split up and moved to Chad or Cameroon.
"The operations especially in forest locations are progressing in defiance of obstacles and landmines emplaced by the terrorists," he added.
But progress has been severely hindered because of improvised explosive devices, a civilian vigilante involved in the operation told AFP in an account backed by a security source.
"Boko Haram have buried landmines all over the routes leading to their camps in the forest, which is no doubt a huge obstacle retarding the military offensive against them," he told AFP.
"We decided to turn back since the route was unsafe. As we were driving back, one of the vehicles carrying CJTF (Civilian Joint Task Force) hit a mine," he added.
"A soldier and three CJTF were killed while another soldier was injured. We trudged along and made it back to Bama yesterday."
The vigilante added: "There are no soldiers in Sambisa right now. We all returned to Bama after the horrifying experience of manoeuvring through minefields."
There was no immediate response from the military, which with its military coalition partners Chad, Niger and Cameroon has driven out Boko Haram from captured towns in recent weeks.
"All their fighters who were pushed out of Bama, Dikwa, Gwoza and Damboa (in Borno state) all moved to Boko Haram camps in Sambisa," he added.
