The group still needs to raise over R100 000 to cover additional costs.
"We are past the point of desperation now," said Levy.
He said while 16 men had been selected for the national team, only 11 players, aged between 19 and 33, were able to pay the initial cost for the trip.
The eighth Touch Football World Cup will be held in Coffs Harbour, Australia from April 24 until May 3.
The three South African teams (men, women, mixed) participating in the tournament are scheduled to compete against 24 other countries.
"I've sent the tournament long e-mails asking for more time to come up with the rest of the money," said Levy.
"We are in desperate need of assistance."
He said the team had started fundraising for the tournament last year, with street events, food stalls, karaoke evenings and golf days.
One team member's parent, a taxi driver, had been driving extra shifts to raise money.
"As a national team, it’s embarrassing to go asking for money."
Since 2010, the men's open team has won 10 trophies.
"In the last World Cup we came third in the mixed men’s division which was excellent," said Levy.
The team trains in Green Point but also holds sessions in poor communities so residents can learn about the game, Levy said.
Team member Adnaan Oesman, 29, who lives in Bo Kaap, said the sport had given him the opportunity to travel both nationally and abroad.
"I’ve been lucky enough to be funded to attend the youth World Cup in 2005 and again in 2011.
"It’s an honour to represent your province and country in these tournaments.
"The sad part is that we have to fund our own trips.
"It's a matter of who can afford to get money together," he said.
Western Province Touch Association chairperson Nicholas Lassen said touch rugby was still an amateur sport in South Africa and was self-funded.
"Money is needed, but a lot more needs to be done by the governing body and the associations.
"The sport has the ability to drastically improve South Africa's rugby skills and ability, and more importantly the SA rugby ladies teams," he said.