The Scottish government said the £428 million Digital Scotland Superfast Broadband (DSSB) scheme is on track to meet its target of 95% coverage by the end of this year.
It said more than 800,000 premises in Scotland can now benefit from fibre broadband following 34,000 connections in the last six months.
DSSB is delivered through two projects, led by Highlands and Islands Enterprise in its area and the Scottish Government in the rest of Scotland.
Funding partners include the UK Government, through Broadband Delivery UK, BT, local authorities and the EU via the European Regional Development Fund.
Across Scotland, around 4,100 new fibre street cabinets are now live and more than 8,700 km of cable has been laid by Openreach engineers.
Rural Economy Secretary Fergus Ewing said: “Fast internet connection is vital to the economic and social wellbeing of our rural communities, supporting businesses and improving lives of local people.
“Last year we made faster progress than any other part of the UK and we are on-track to meet our Programme for Government commitment of 95% coverage by the end of this year.
“However, these upgrades are not automatic.
“I would encourage more people to check whether they are eligible on the DSSB website and contact a service provider of their choice to start receiving faster broadband.
“I am not complacent – I am aware that those who do not have access are at a disadvantage and our job is not done until everyone is connected. We are now focussing on the next steps to achieve 100% coverage by 2021.”
Robert Thorburn, Openreach digital partnership director for Scotland, said: “We’re working flat out to bring high-speed fibre broadband to as many Scottish communities and households as possible and we’re continuing to make good progress.
“It’s fantastic to be reaching smaller communities such as Gairloch, Drummore and Ballantrae and it means many people in these places can now order their fastest-ever broadband speeds from a wide range of providers.
“With around a third of homes and businesses having upgraded to fibre so far, there’s plenty of scope for more Scots to benefit from these much faster speeds.”
UK Minister for Digital Matt Hancock said: “I’m delighted that more than 800,000 Scottish homes and businesses have now had their internet speeds boosted as part of our UK wide rollout of superfast broadband.
“By the end of this year 95 per cent of UK properties will have access to superfast speeds, but more needs to be done to make sure no-one is left behind.
“We know just how important broadband is in the digital age, and we’ll continue to support Digital Scotland delivering on the ground so that by 2020 everyone in Scotland, and the rest of the UK, will have access to a fast, reliable and affordable internet connection.”