Attractions such as Edinburgh Castle and Linlithgow Palace boosted the June to August total by 14.8 per cent, compared with last year.
The Scottish Government agency, which is Scotland’s biggest operator of visitor attractions with 78 sites, clocked up a total of 1,692,611 visitors.
The figures, which had surpassed expectations, were boosted by more direct flights, more Chinese and Russian tourists and Scots making more trips to historic properties.
Edinburgh Castle had its busiest summer, with 229,940 visitors in August setting a new monthly record and nearly 36 per cent higher than a year ago.
The castle saw overall visitor numbers increase by 26 per cent over the three months on 2012.
Linlithgow Palace, where Mary, Queen of Scots was born, welcomed a record 37,548 visitors over the summer – up 36 per cent on last year.
The rise followed widespread publicity for the Chanel Métiers d’Art fashion show there last December, which featured Scots supermodel Stella Tennant.
St Andrews Castle also had its highest summer total, up 9.3 per cent to 32,867, and another record-breaker was Tantallon Castle in East Lothian, up by 17 per cent to 17,678.
There was similar strong growth at Iona Abbey, which in July marked the 1,450th anniversary of the arrival of St Columba from Ireland, with a 13.5 per cent increase to 34,957.
Historic Scotland said overall income from group visits of more than ten people was up by 41 per cent on last year, with Edinburgh Castle seeing a 69 per cent increase in such visits in July.
However, it said other, less accessible rural properties had suffered falls in visitor numbers, with Stanley Mills in Perth down by 28 per cent to 3,374.
Cardoness Castle, near Kirkcudbright in Dumfries and Galloway, saw its total tumble by 26 per cent to 2,171, while Bonawe Iron Furnace, near Oban, was down 24.2 per cent to 1,940.
An agency spokeswoman said: “We find with some of the more remote sites that factors such as high petrol prices and perceptions that they are not as easily accessible as some of the other properties can be a factor.”
Stephen Duncan, director of commercial and tourism for Historic Scotland, said it had not expected such growth overall.
He said: “Last year saw a flattening out of visitors, due to a combination of severe weather and displacement of the travel trade. We had always expected 2013 to see a return to previous levels, but the summer performance has surpassed all expectations.
“It’s particularly encouraging to see patterns at Edinburgh Castle, Scotland’s No1 paid-for tourism attraction, replicated at many of our other properties across our estate.”
Culture secretary Fiona Hyslop said: “These figures illustrate the important role that heritage plays for modern-day Scotland. The benefits are many, in terms of highlighting our diverse culture both at home and abroad, but also in terms of supporting and driving economic growth.”
There are signs that other visitor attractions have also had a bumper summer.
The National Museum of Scotland in Edinburgh said yesterday its Mary, Queen of Scots exhibition had clocked up 37,000 visitors in two months, making it the museum’s busiest show since it reopened in 2011.