Official figures show a sharp rise in the number of incidents -- up 8% on the previous year.
There was also another rise the number of male victims. One in every seven cases of domestic abuse is now against men.
It comes against a worrying a shortage of places in refuges. A snapshot survey carried out found that more than half of the women who requested a safe place to shelter from an abusive partner had to be turned away.
Women’s Aid, which commissioned the research, said it raised serious concerns about provision for women who may have gone to great lengths and needed considerable courage to leave their partner, only to be turned away at the door.
Lily Greenan, head of Scottish Women’s Aid, said: "There is a straightforward issue about space and demand and real problems highlighted with the availability and accessibility of refuges.
"Being turned away will prove a huge disincentive for women trying to escape abusive relationships.
"The message for women is: Keep trying. Don’t give up. The message for the Scottish Government and local authorities is that we need more resources than we have got.
"No-one wants to hear that in a recession, but giving these women a safe haven with privacy and dignity is vital. We are just not there yet."
Labour deputy leader Johann Lamont called for special courts to deal with domestic abuse cases to be set up across Scotland.
Ms Lamont said the increase in incidents was "of obvious concern" but added: "I hope that at least part of the rise can be attributed to an increase in the confidence of victims to come forward."
The Women’s Aid study found that on one day in September there were 365 women and 360 children in refuges across Scotland.
Some 47 women requested refuge that day but 12 women and five children were denied access due to a lack of space.
Some 19 of the women had problems accessing a refuge because of a lack of public transport or because they had no access to welfare benefits. Women earning over a certain amount or with uncertain immigration status do not have access to refuges.
A Scottish Government spokeswoman said: "Any woman who has to flee her home because of domestic abuse is entitled to accommodation.
"There is a statutory duty on local authorities to provide accommodation, whether that is in a refuge, flats or purpose-built accommodation.
"On top of local authority budgets, the Scottish Government is investing £675 million this year in affordable house building, including building new refuges.
"Just a few months ago, two new state-of-the-art refuges opened in Drumchapel and East Lothian, with individual flats, games rooms for children and counselling services. We are committed to providing funding for new projects."
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