Mr Mackay said the situation was “fluid” as he unveiled a raft of measures to enhance public transport links and pleaded with commuters to consider car-sharing, working from home and avoiding peak times.
Today is set to be a major test for the transport network as the Christmas period gets into full flow and commuters begin the working week.
On a typical weekday, an average of 70,000 vehicles use the Forth Road Bridge, and at peak morning time around 6300 vehicles cross the structure southbound.
Mr Mackay conceded that around 2000 cars might not be absorbed by the transport network despite the emergency alternative travel arrangements unveiled yesterday.
He said: “What’s hard to predict is how many people will still choose to drive at that point considering the public information that’s out there, the alternatives that are in place and the advice that’s been given. It will be unpredictable because of the different choices that people will make.”
Scotrail will provide an additional 6500 seats by pulling carriages from other services and taking trains out of refurbishment programmes, increasing its capacity by 40 per cent.
Stagecoach will put on 33 extra buses – equating to 11,000 more seats – as part of a park-and-ride priority service between Fife and Edinburgh.
Free frequent shuttle buses will also run between Inverkeithing Railway station and Ferrytoll park and ride to provide extra parking for those taking trains.
To help cope with demand, the A965 between Cairneyhill and Longannet in Fife was to become a priority-only route for buses and HGVs from 4am this morning.
Buses will also be given priority on the Kincardine Bridge, however the crossing will also be open to other traffic.
A “comprehensive” new website dedicated to travel options for Forth Road Bridge users was launched yesterday.
Mr Mackay insisted that the 20mm-wide crack in a steel truss under the southbound carriageway, which prompted the closure last week, was only found on Tuesday and said the decision to shut the bridge until the New Year had been the right thing to do.
Further assessments are being carried out on the bridge and engineers have been “working around the clock” on the design and repair.
A round-table discussion will be held tomorrow to assess how to further ease the disruption, while routes and transport will be constantly reviewed to help support people on their journeys.
On Friday, the first full day of the closure, there were 11-mile rush hour tailbacks.
Mr Mackay warned that the diversion routes would be slow-moving. He said: “The Forth Road Bridge carries 100,000 people on a typical weekday. We know it will be under considerable pressure with that displacement. I would encourage people to use public transport with the enhancements that we have been able to put in place.
“These will only be effective if we have the support of the public. Through carefully planning journeys, considering travelling at different times or considering other options such as car sharing and working from home, even though there will still be delays, we can all work together to come through this challenging situation.”
He said the Scottish Government was liaising with the business community and the UK government to try to mitigate the impact.
The Anniesland-Glasgow Queen St, Falkirk Grahamston-Glasgow Queen Street via Cumbernauld, Glasgow-Kirkcaldy/Markinch, and Glasgow-Dundee train services have been cancelled or reduced in frequency, with passengers advised to take replacement bus services or alternative train routes.
Phil Verster, managing director of the ScotRail Alliance said: “These are exceptional circumstances and we have taken exceptional steps to address them. We want to help keep Scotland moving during the bridge closure. With the measures we are announcing, I hope we can achieve that.
“By bringing in other trains from across the UK, pulling trains from our major refurbishment programme and, regrettably, moving a small number of trains from other parts of the network, we have managed to add an extra 40 per cent capacity on our trains in and out of Fife.”
Mr Verster said he appreciated that people may miss their usual trains but that the firm had tried to keep the impact as minimal as possible.
Sam Greer, Stagecoach regional director, said his staff were doing “all they can” to help ensure people have smooth journeys.
The park-and-ride journeys between Fife and Edinburgh will take two hours and will be provided a reduced fare price of £3 for an adult return.
He said: “We hope these extraordinary measures will encourage more people to travel by public transport, reducing congestion on the roads and helping everyone continue to travel in the run-up to Christmas.”
Assistant Chief Constable Malcolm Graham, of Police Scotland, said roads officers would be working alongside Amey traffic management staff along all affected routes and in the Traffic Scotland control centre.
He added: “We will be deploying further road policing officers to patrol the diversionary routes and affected parts of the road network to assist in keeping the traffic flowing. We do expect a certain amount of delays, but will continue to assess and adapt accordingly to help traffic keep moving.
“I would urge anyone who needs to travel tomorrow morning to plan ahead – consider public transport, check the weather conditions and leave plenty of time for your journey. Many people will be driving on unfamiliar, busy roads and so please take extra care.”