The British rider was active throughout, starting an early but futile breakaway attempt. The decisive move came with 19 laps to go when Bobby Lea (USA) and Jasper de Buyst (Belgium) went away and started working well together.
Roger Kluge (Germany) and Lasse Norman Hansen (Denmark) chased and briefly made the breakaway a group of four, before going away from the original leaders. The German-Danish duo lapped the field and sat in until the end.
Thomas Boudat (France) and Glenn O'Shea (Australia) were left in no man's land, almost a lap up on the field but unable to get on the back of the pack.
Cavendish contested the sprint, taking second from the bunch, but due to the four riders ahead he took sixth from the opening event. Fernando Gaviria (Colombia) pipped the Manxman to the line for fifth.
Two more events remain on the first day of the omnium, with the individual pursuit followed by the elimination race.
More from the Olympics
All you need to know about the omnium
Men’s omnium: 15km scratch race
1. Lasse Norman Hansen (DEN)
2. Roger Kluge (GER)
3. Thomas Boudat (FRA)
4. Glenn O’Shea (AUS)
5. Fernando Gaviria (COL)
6. Mark Cavendish (GBR)
7. Elia Viviani (ITA)
8. Gael Suter (SUI)
9. Park Sanghoon (KOR)
10. Dylan Kennett (NZL)
11. Tim Veldt (NED)
12. Artyom Zakharov (KAZ)
13. Kazushige Kuboki (JPN)
14. Ignacio Prado (MEX)
15. Gideoni Monteiro (BRA)
16. Leung Chun Wing (HKG)
17. Bobby Lea (USA)
18. Jasper de Buyst (BEL)
Thank you for reading 20 articles this month* Join now for unlimited access
Enjoy your first month for just £1 / $1 / €1
*Read 5 free articles per month without a subscription
Join now for unlimited access
Try first month for just £1 / $1 / €1