Statistics released by ISD Scotland showed a 10 per cent fall in the last year in meeting the target for key diagnostic tests, including procedures to detect cancer.
The Scottish Government has said patients should wait no longer than six weeks for eight diagnostic tests including MRI scans.
Only 82.9 per cent of patients waited less than six weeks in June compared to 92.2 per cent at the same time last year.
Over the same period the number of patients waiting more than six weeks has increased from 4,800 to 13,600.
Ms Robison reacted to the figures by announcing the creation of an expert group to cut waiting times.
The data also showed that in June the 18-week referral to treatment target was met for 84.8 per cent of patients, down from 87 per cent in the same month last year.
Only five out of 15 health boards achieved the 90 per cent standard, which has not been met nationally since June 2014.
Figures also show that in the three months to June, 81.4 per cent of patients waiting for either inpatient or day treatment were seen within the 12-week treatment-time guarantee.
It compares to 82.2 per cent in the previous quarter and a more dramatic fall from 91.3% in the same period last year.
Meanwhile, 74 per cent patients waiting for a new outpatient appointment at June 30 had been waiting 12 weeks or less, down from 80.7 per cent at March 31 and 85.7 per cent at the same point last year.
Labour health spokesman Anas Sawar said: “This cannot go on. If Nicola Sturgeon is planning a reshuffle she should move Shona Robison from the health brief and send a message that she is finally willing to give the health service the support it needs.”
Gregor McNie, Cancer Research UK’s public affairs manager for Scotland, said the increasing number of patients waiting more than six weeks for an endoscopy was of particular concern.
The number patients waiting more than six weeks had risen from 2,563 to 8,362 over the last year.
Mr McNie said: “It is extremely worrying that the NHS in Scotland is failing to cope with the increased demand for diagnostic tests, and patients are continuing to suffer. The rapidly diminishing performance in endoscopy services is of particular concern. This must be addressed as a priority.
“Patients must be diagnosed and treated early if they are to have the best chance of surviving cancer. Waiting so long for tests adds to the anxiety anyone who has possible cancer symptoms feels.”
Shadow Health Secretary Miles Briggs said the waiting figures were a “disgrace”.
“It’s becoming increasingly difficult to find an NHS target the SNP does consistently hit,” Mr Briggs said. “Its stewardship of the health service has been nothing short of a disgrace, and patients right across the country are suffering as a result. The Lib Dem health spokesman Alex Cole-Hamilton said the Scottish Government’s treatment time guarantee was “not worth the paper it is written on”.
He said: “Responsibility for the waiting times crisis lies squarely at the door of SNP ministers. They ignored warnings of an NHS recruitment crisis and failed to deliver a step change in mental health.”
Ms Robison’s Elective Access Collaborative Programme will bring together experts from the Scottish Government, NHS Scotland and the Royal Colleges – to provide support to health boards.
It will be led by the Chair of the Royal College of Physicians of Edinburgh, Professor Derek Bell, and the Chief Executive of NHS Fife, Paul Hawkins.
The Health Secretary said: “We know that any patient waiting for planned surgery or an outpatient appointment wants to be seen as quickly as possible.
“Today’s announcement will build on our earlier injection of funding to reduce waiting lists, by providing the expert support to transform scheduled care and put the services on a sustainable footing for the future.”