The latest Audit Scotland review of the £412 million project shows a target to deliver access to a broadband network to 95% of homes and businesses by December 2017 is likely to be met.
However, the remaining areas are more rural and remote and “likely to need more complicated and costly engineering solutions”, the report said.
Rural premises are also currently receiving lower average broadband speeds than in other areas.
The Scottish Government and Highlands and Islands Enterprise (HIE) appointed BT to extend Scotland’s fibre broadband network in 2013.
Audit Scotland said 2.2 million out of 2.6 million homes and businesses (86%) had access to fibre broadband by March this year, 1% more than the original target.
The report said: “While 26 of Scotland’s 32 council areas have met contractual targets for fibre broadband coverage, the areas that remain are rural or remote and are likely to need more complicated and costly engineering solutions.”
These include Highland, Orkney, Shetland and the Western Isles.
Caroline Gardner, Auditor General for Scotland, said: “Fast, reliable internet access is increasingly essential for everyday life so it’s encouraging to see good progress being made in rolling out fibre broadband.
“However, there is a lot still to be done by the Scottish Government if it is to achieve its vision of a world-class digital infrastructure, particularly in improving download speeds in rural areas.
“It’s important that it continues to monitor the cost and progress of broadband roll-out so that these communities aren’t excluded.”
Audit Scotland said the Scottish Government must now decide how to spend a further £42 million available for extending broadband coverage.
Rural Economy and Connectivity Secretary Fergus Ewing said: “I welcome today’s Audit Scotland report, which outlines the good progress we are making in widening the access to high-speed broadband and confirms that 86% of premises across Scotland now have access to fibre broadband - 1% more than our original target.
“However, we also recognise that there is much more we can do at a Scotland-level to extend coverage, particularly to rural areas.
“That is why we have made the commitment that 100% of properties across Scotland will be able to access superfast broadband by 2021, and I will outline next steps later this year.”
Scottish Conservative connectivity spokesman Jamie Greene said: “It is encouraging that some progress has been made on the roll-out of superfast broadband but it is clear there is still a lot of work to do.
“The remainder of the roll-out seems to be more challenging, complicated and costly but people deserve realistic, properly-funded and achievable guarantees on when this so-called superfast broadband is coming.
“I suggest that every potential technical solution to reach difficult-to-connect rural areas is put on the table.”