Rhoda Grant MSP's member's bill proposes to increase access to justice for victims of domestic abuse and enable police and prosecutors to provide a more robust response to breached civil protections orders.
The Justice Committee had already recommended that the parliament agree to the general principles of the bill.
But the committee did not support making legal aid free to all for applications to a civil court for an interdict with a power of arrest, or a non-harassment order, where domestic abuse was involved.
Community Safety Minister Fergus Ewing vowed to work with Rhoda Grant to improve her bill, in the interests of protecting victims of domestic abuse.
He said domestic abuse was "abhorrent and a stain on Scotland", saying there were over 51,900 incidents of domestic abuse recorded by police in 2009 - 10.
The Conservatives pointed out that the part of her bill which allowed legal aid to be sought by domestic abuse victims without means testing could contravene human rights law.
The minister echoed this concern, saying he thought there were "compelling" reasons to drop this section of Ms Grant's bill.
Like all the parties, Mr Ewing agreed to the aspect of the bill which made breaching an interdict order a criminal offence.
However the minister said the definition of domestic abuse in the bill was too wide, but he assured Ms Grant that he, and the Lord Advocate would work with her until a workable definition was reached.