The Tamil National Alliance (TNA) said 1,474 people owning land in Jaffna filed the cases challenging the attempts to illegally and unlawfully acquire their private land.
"The petition challenges the notices issued under the Land Acquisition Act which specifies that 6,381 acres and 38.97 perches are to be acquired. The massive area that is identified constitutes approximately 25.8 sq km," the TNA said.
The TNA said the petitioners owned substantial tracts of land that fall within the area being acquired by the government and were displaced from their land due to the war.
"Although the war ended in 2009, the petitioners have been prevented from returning to their land due to the military occupation of the area and barbed wire fences and barricades manned by the military," said the TNA.
Thousands of Tamils were displaced from the north during the 30 year war between the Tamil Tigers and the military.
Hundreds fled to neighbouring India while others either moved to other parts of the country or settled overseas.
However, with the war ending in May 2009 following the defeat of the rebels, land owners have begun to return and are seeking ownership of their property.
The Sri Lankan government says most property held by the military during the war had been returned while some areas are still with the military owing to security reasons.