There was no immediate comment from Liberation Tigers of Tamil Eelam(LTTE) rebels regarding the pass, which they have controlled since April 2000.
If confirmed, the government's advance would deal another serious blow to the group by further isolating the rebels in a section of northeastern coastal jungle around Mullaittivu, the last remaining town in the hands of the LTTE.
"We are taking the offensive to the Mullaittivu jungles where [LTTE leader Velupillai] Prabhakaran is hiding," Jagath Dias, an army major general, said on Monday.
The pro-rebel Tamilnet website said Tigers were putting up stiff resistance to the military advance on Mullaittivu and said they killed 53 soldiers and wounded another 80.
Military officials denied the rebel figures and said security forces recovered the bodies of 12 Tiger rebels.
Tens of thousands of people have been killed since the Tamil Tigers started fighting government forces in the 1980s, seeking a separate homeland for ethnic Tamils.