"We want them to feel at home here," Eduardo Paes said. "I almost feel like putting a kangaroo to jump up and down in front of their building."
The Australian Olympic Committee said in a statement Sunday
that its athletes are staying in hotels rather than the village due to the condition of the official accommodation.
Responding to Paes' offer, Australian committee spokesman Mike Tancred told a Brazilian newspaper
"we do not need kangaroos, we need plumbers to account for the many puddles found in the apartments."
"Due to a variety of problems in the Village, including gas, electricity and plumbing I have decided that no Australian Team member will move into our allocated building," Australia's Chef de Mission Kitty Chiller said.
"Problems include blocked toilets, leaking pipes, exposed wiring, darkened stairwells where no lighting has been installed and dirty floors in need of a massive clean. In operations areas water has come through the ceiling resulting in large puddles on the floor around cabling and wiring."
In a statement
, the International Olympics Committee (IOC) and Rio 2016 said the issues were being addressed but the village was still several days away from being completed.
The British Olympic Association acknowledged that while there were some "maintenance difficulties" with the village, the first Team Great Britain athletes will begin moving in on Tuesday.
"Some (countries) are comfortable for their teams to move in, and I envy them," said Chiller on Sunday
"We are reasonably confident we will be able to enter the village on Wednesday."
Numerous safety concerns have been raised ahead of the start of the 2016 Olympics on August 5, including the threat of international terrorism
and high crime levels in the host city.
One foreign athlete living in Rio allegedly got a taste of that crime on Saturday.
New Zealand jiu jitsu athlete Jason Lee said on Facebook that he was "kidnapped" by armed men in military police uniforms and forced to withdraw cash from two separate ATMs.
Jiu jitsu is not an Olympic sport, so Lee is not competing in the Games, but the former national jiu jitsu champion has lived in Rio for almost a year.
"I was threatened with arrest if I did not get in their private car and accompany them to two ATMs to withdraw a large sum of money for a bribe," he said on Facebook
"I'm not sure what's more depressing, the fact this stuff is happening to foreigners so close to the Olympic Games or the fact that Brazilians have to live in a society that enables this ... on a daily basis."
He told New Zealand's Fairfax Media
that he "feared for his life" during the alleged incident. Lee's girlfriend, a reporter for Fairfax, said on Twitter
that the pair had reported the incident to police.
Rio police could not immediately be reached for comment.