This is according to the submission made on Friday by the SCVO to the commission, led by Lord Smith of Kelvin, which will produce recommendations for further devolution by 30 November.
The submission draws on feedback from representatives of more than 100 third sector organisations and gives 14 specific powers that should be devolved to Scotland.
It notes that charity regulation is carried out at a devolved level by the Office of the Scottish Charity Regulator, as are some aspects of fundraising regulation such as street collections, whereas others are regulated on a UK-wide level, such as fundraising standards, which are overseen by the Fundraising Standards Board, and charitable tax reliefs, which are administered by HM Revenue & Customs.
Regarding fundraising regulation, the submission says: "We favour consistency with Scottish charity regulation and consider we need the relevant powers devolved in order to achieve this. However, it must be recognised that some charities have an interest in maintaining UK-wide consistency for fundraising rules, in some cases to support cross-border fundraising."
The SCVO submission also says that the commission should consider further devolution of charitable tax reliefs.
If, as proposed by some political parties, income tax were to be devolved, then tax reliefs including Gift Aid, social investment tax relief and inheritance tax "must also be devolved to ensure consistency", it says.
"These reliefs would need to be devolved in full, giving Scotland the power to redesign the schemes and not just deliver the existing UK systems," it says.
This would also create consistency with the remit of the OSCR. The submission says: "It is evident that we need to give primacy to Scottish legislation when it comes to ensuring public trust in the charity brand in Scotland."
It says VAT relief schemes for charities should be devolved. "We believe that the devolution of VAT relief schemes offers a real opportunity to better reflect Scotland’s unique geography, demography, public service mix and national ambitions," it says.
Other devolved powers the SCVO asks for include welfare, consumer protection, energy and "those aspects of employment law that directly affect devolved powers such as social care and childcare". It also says the civic energy and debate generated in the run-up to the independence referendum in September should be harnessed.
John Downie, director of public affairs at the SCVO, said: "The sector wants to see a commitment to more powers being devolved to communities so that they have a say in the decisions that affect their lives.
"This would mean that, despite the Smith Commission’s impossibly tight timetable, we can still pursue a bottom-up devolution process led by people in Scotland, not just by politicians."