Hape said since Friday night the refuge had responded to five high-risk calls needing safe house accommodation, and at least seven others for assistance with safety plans.
Some victims may be forced to remain with abusers until a safe place could be found, she said.
Despite this desperate situation, Hape said the amount of baseline funding received from the Ministry of Social Development had not increased since 2008.
The refuge was paid $21.25 an hour to run a 24-hour crisis line, a safe house shelter and community support services such as counselling and child advocacy.
In the 15 months from July 1, 2016, the refuge dealt with more than 1000 crisis calls and more than 6000 other calls for support and advice. It is funded for 320 crisis calls a year.
Hape said without the community the refuge could not continue to keep its doors open.
In a written statement, Ministry of Social Development acting group manager Kelvin Moffatt said the Ministry was concerned to hear about this level of demand.
"We will contact Hazel Hape to talk over what options she has available, and if we are able to help," he said. Hape confirmed the Ministry had called her yesterday.
Labour list MP Angie Warren-Clark, who was the manager of the refuge until becoming an MP, said the government was undertaking a review of spending in a number of areas but the process would take some time.
The Government was "absolutely committed" to funding crucial intervention services across the country, such as Tauranga Women's Refuge, she said.
Tauranga MP Simon Bridges said the work Tauranga Women's Refuge and others did to support domestic violence victims to get their lives back into shape was crucial.
He would support the call for funding for a second refuge safe house in Tauranga if the numbers showed another one was needed.
Shakti Women's Refuge Tauranga's co-ordinator Lisa Angraeni said while the refuge was not yet full, traditionally they experienced an influx of clients in the coming week.
"We're facing the same funding issues as Tauranga Women's Refuge ... But the hardest thing for us is that MSD only provides funding for New Zealand citizens and residents."
"That means non-residents often have to stay with us a lot longer," she said.
Western Bay police area commander Inspector Clifford Paxton said police would work with victims and partner agencies to ensure suitable support and safety plans were in place for those identified at risk.
Anyone who feared for their own or someone else's safety should dial 111.
If you're in danger now:
Phone the police on 111 or ask neighbours or friends to ring for you. Run outside and head for where there are other people. Scream for help so that your neighbours can hear you. Take the children with you. Don't stop to get anything else. If you are being abused, remember it's not your fault. Violence is never okay.
Where to go for help or more information:
Women's Refuge: Free national crisis line operates 24/7 — 0800 refuge or 0800 733 843
Shine, free national helpline 9am- 11pm every day — 0508 744 633
It's Not Ok: Information line 0800 456 450