The British number one reached a career-high ranking of 23 after making his first ATP Tour final in Marrakesh at the weekend, but a positive week ended on a sour note when he was well beaten by lowly-ranked Pablo Andujar.
He seemed to carry that disappointment, and no doubt a little weariness, into the first set against Seppi and trailed 5-1 after a lacklustre first six games.
Edmund rallied at the end of the set and finally made his sixth break point of the second count to force a decider but Seppi, who was one of the Yorkshireman's victims during his run to the Australian Open semi-finals, finished the stronger to win 6-3 5-7 6-2.
Seppi's reward for beating Edmund is a second-round meeting with Guillermo Garcia-Lopez.
Elsewhere, Dominic Thiem recovered from losing the first set to beat Andrey Rublev to reach the third round.
Rublev took the first set 7-5 before the fifth seed from Austria took the second and third sets by the same score. Thiem will play either Novak Djokovic or Borna Coris.
David Goffin is also through to the third round after beating Stafanos Tsitsipas 7-6(7/4) 7-5.
Grigor Dimitrov was pushed all the way by Pierre-Hugues Herbert who took the first set 6-3 before Dimitrov took the second and third sets 6-2 6-4.
Alexander Zverev booked his place in the third round after beating Gilles Muller 4-6 6-3 6-2.
Zverev saved a break point in the first game of the final set and broke Muller in the second to take control of the deciding set.
Mischa Zverev, older brother of Alexander, will meet either Richard Gasquet or Diego Schwartzman after beating seventh seed Lucas Pouille 2-6 6-1 7-6(7/3) in the second round.
Gasquet reached the second round after beating Jeremy Chardy 6-4 7-6(7/5) while Schwartzman came from a set down to beat Guido Pella in an all-Argentina first-round match.
Wildcard Gilles Simon knocked out 16th seed Adrian Mannarino 6-3 4-6 6-2 to set up a second-round clash with Karen Khachanov.
Italy's Fabio Fognini beat Ilya Ivashka in straight sets to set up a second-round meeting with Jan-Lennard Struff who eased past Japan's Yuichi Sugita 6-3 6-2.
Qualifier Marco Cecchinato continued his impressive form beating Damir Dzumhur 6-3 6-2 to set up a second-round tie with Milos Raonic.
Feliciano Lopez lost the first set to Benoit Paire before recovering to win the next two sets 7-6(7/5) 6-4 to set up a second-round tie with Roberto Bautista Agut.
Fernando Verdasco will play Marin Cilis for a place in the third round after beating Pablo Cuevas 5-7 7-6(7/4) 6-1.
Philipp Hohlschreiber will play Albert Ramos-Vinolas in the second round after beating Tennys Sandgren 6-2 6-2.
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