As many as 400 elephants have crossed the Zambezi River, which separates Zambia from northern Zimbabwe, in recent months, said Johnny Rodrigues, head of the Zimbabwe Conservation Task Force.
Three elephants also roamed into the eastern border city of Mutare this month and state wildlife authorities "want to shoot them before they kill somebody," he said.
The task force and a Zimbabwe animal group received official authority to capture and transport the elephants to Chipinda Pools, believed to be their original home area 125 miles to the south.
"The problem is funding for the relocation," Mr Rodrigues said. State game rangers "won't wait much longer before destroying the elephants."
He said changes in Zimbabwe's countryside had also forced a leopardand its cub out of its natural habitat and into an upmarket Harare suburb.
Mr Rodrigues said the task force set up drugged, baited traps for predators so they could be returned to the wild, but none has been caught since a guard dog was attacked earlier this month.
The independent task force has appealed for more action - and money - to preserve the troubled nation's wildlife.
In Zimbabwe's economic meltdown, "humans are encroaching more and more into areas previously reserved for wildlife," the task force said.
Tourism and photographic safaris have dropped sharply during years of political and economic turmoil since the often violent seizures of thousands of white-owned farms began in 2000, disrupting the agriculture-based economy in the former regional breadbasket.
Longtime ruler President Robert Mugabe blames Western sanctions for the economic crisis that has led to acute shortages of food, gasoline and the most basic goods.
Poaching of small animals has intensified, with villagers torching the bush to drive even rodents and rock rabbits into traps for food, conservationists say.
Mr Rodrigues said more animal fencing was needed at wildlife preserves to combat poaching and the escape of animals from their natural habitat after being made skittish by gunfire.
Conservationists already have raised the alarm for Zimbabwe's rare rhinos after a sharp increase in poaching over the past year because of a breakdown of law enforcement in the country.