Organisers said the first leg would now start at 0930 local (0530 GMT) instead of 1100.
The second leg has also been rescheduled for 1300 local.
The Alpine centre above the resort of Rosa Khutor was shrouded in cloud and fog on Monday with athletes doing some free skiing on training slopes.
Some biathlon and snowboard cross events were postponed on Monday due to poor visibility.
The Alpine skiing speed events have all been completed, leaving only the men's and women's giant slaloms and slaloms - four technical races in all - for the final week.
- Sports & Recreation
- Rosa Khutor