The announcement means that vans and other light goods vehicles will be allowed to use the A985 priority corridor between Rosyth and Kincardine while the Forth Road Bridge remains closed.
Changes to the travel restrictions will also mean vans will be able to use the bridge and the A985 corridor from Monday.
The A985 had previously been used by heavy goods vehicle and buses only.
However, restrictions to the A985 priority route will be lifted completely on 23 December for the holiday period, Mr Mackay said.
He said: “Since the closure of the bridge and the publication of our travel plan to mitigate its impact, we have been monitoring performance and listening to our stakeholders, including communities and business organisations.
“Clearly the closure of the bridge has had a significant impact, particularly on small and medium sized businesses, and we and our transport partners have been listening to business community views since the travel plan was implemented.
“To address their feedback, from this Monday all commercial light goods vehicles will be allowed 24 hour a day access to the A985 priority route.
“We have also responded to community needs, and so can confirm that all vehicles will have access to the priority route at weekends and outside peak periods on weekdays.
“We also intend to lift restrictions on the priority route completely on the 23rd of this month to coincide with the start of the holiday period.”