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Defence officials say the animals are near starvation. They have asked the local authorities for permission to cull almost half the area's population.
Campaigners claim there is no evidence of starvation, and have pledged to protest if the cull is approved.
Canberra's local government is deciding whether to grant a shooting licence.
"Our concerns are for the welfare of the animals and the potential for a starvation event," city official Russell Watkinson told ABC radio.
The defence department already runs a pilot scheme using food laced with contraceptives to try to thin the kangaroo population in the area.
But military officials say the problem near their Majura training area is so severe that they cannot wait for the scheme to take effect.
They want to shoot 3,200 common grey kangaroos by July.
Mary Hayes, of local campaign group Animal Liberation, said a cull would burden the Australian Capital Territory (ACT) with a worldwide reputation for cruelty.
"It is a very cruel, violent way to treat animals - on a par to just treating them as if they were weeds to be mown or pulled out," she said.
And Pat O'Brien, another wildlife campaigner, said the cull plan was "just an excuse to kill them".
"If they go ahead with it, they are going to be sorry. We will do whatever it takes to stop this," he said.
According to the ACT's government, the Canberra area contains the densest populations of kangaroos ever recorded.
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