It was revealed that FAIs in Scotland are taking up to three years to start, even when criminal investigations are not active.
When criminal investigations are being conducted, FAIs can take up to six years to establish.
New Scottish Government proposals for the FAI system launched last week have been criticised as they contain no measures to allow decisions on FAIs to be speeded up during criminal proceedings.
In one of the worst cases, the families of three men who died after the Flying Phantom tug boat capsized on the River Clyde have waited more than six years for a decision on whether there will be an FAI, which seeks to find lessons to be learned from fatalities, while proceedings are continuing.
It has now emerged the Crown Office, concerned about the speed it takes to establish FAIs, is to examine what can be done to make proceedings quicker.
The review is not expected to tackle issues around whether FAI investigations can take place alongside any criminal probe, which the Crown Office always sees as taking precedence.
A Crown Office spokesman said: "Carrying out thorough investigation is the only way to ensure proper decisions can be reached to hold Fatal Accident Inquiries. We will not compromise thoroughness for speed, however, the Law Officers share the public's concern about the length of time it can take to hold an FAI and believe more can be done to reduce delays in investigations.
"Although many of the delays in the FAI process are outwith the control of the Crown, the Law Officers recently ordered a review into the Crown's internal FAI process in an attempt to identify ways of shortening the process within the Crown Office and Procurator Fiscal Service."
There are 50-70 FAIs per year but more than 13,000 deaths are reported to procurators-fiscal annually. The Lord Advocate issued guidance to all procurators- fiscal last December that a petition should be made to the relevant court within two months of receiving crown instruction to hold an FAI.
The Crown Office says it has implemented all six recommendations made by Lord Cullen, who carried out a review of the FAI system in 2009.
They include establishing a central FAI team led by an advocate depute or a senior prosecutor, which will oversee and track progress over all cases in which an FAI is mandatory or is likely to be recommended.
"Strict timescales have now been set to ensure we initiate court proceedings as soon as possible after a decision is taken to hold an FAI, which we hope will lead to fewer delays in securing court accommodation," the spokesman added.
"FAIs are extremely complex to investigate and are likely to involve lengthy expert investigations by regulatory authorities and or criminal proceedings. The Crown's role can only begin after other agencies have completed their enquiries which means we do not have control of the entire process.
"Where we can take steps to help speed up the process without compromising its thoroughness we are absolutely committed to doing so.
"The Crown Office understands families want answers as soon as possible. We are committed to ensuring their loved one's death is properly investigated. While that will often take time we will ensure they are kept fully informed throughout the process and that reasons for any delays are fully explained."