Members of the RMT have staged walkouts on seven days in the last month, with three more stoppages planned for Thursday, Saturday and Sunday.
The union is in dispute with ScotRail over staffing concerns on new trains.
Transport Minister Humza Yousaf said planning was "well-advanced" in order to minimise any disruption caused by the strike action.
The RMT said it had "the overwhelming support of the Scottish people".
The transport minister said ScotRail was offering an "enhanced timetable above the regular provision".
Mr Yousaf added: "More services and carriages will run between Glasgow Central and Troon throughout Thursday to Sunday to allow the vast majority of people to travel to and from the venue with minimum disruption to travel plans."
However, ScotRail has said some trains to Glasgow from other parts of Scotland would have a reduced service and different departure times.
Those travelling to The Open were advised to check the ScotRail website or app for the latest updates and leave extra time for their journey.
The ongoing dispute with the train operator and RMT union concerns the operation of train doors by drivers instead of onboard conductors.
The union said it was defending its policy of no extension of driver-only trains and for guards to be in control of operating doors.
ScotRail has insisted there will be no job losses or pay cuts with its proposed changes.
Mr Yousaf added: "These strikes are disrupting passengers and affecting the reputation of Scotland's railways, and they should be suspended to allow talks to conclude and a way forward agreed."
RMT general secretary Mick Cash said: "The minister and his colleagues in the Scottish government need to remember that this dispute has been created byAbellio/ScotRail via Transport Scotland on behalf of his own administration who have the power to sort it out.
"RMT has been engaging with the public over the last eight weeks and we have the overwhelming support of the Scottish people who want to see a safety-critical guard on our services and not this watered down version of scheduling a second person on the train who has no safety-critical function and who can be removed at the drop of a hat."
ScotRail has said train services to the Open Golf Championship in Troon will run despite ongoing strike action.