The former world number one made his return from a groin injury with a training week and two doubles matches in Rome and had been expected to play singles next week.
But The Scotsman understands he is still feeling some discomfort and has headed back home for more rehab and to begin training on his favourite surface, with full fitness for Wimbledon now the clear goal.
Murray had been planning to take a wild card into one of the ATP tournaments in Geneva or Lyon next week but it emerged on Saturday that he had turned one down for the Swiss event, raising serious questions about his prospects of playing at Roland Garros.
The Scot – who has played just one match on clay since 2017 – had entered qualifying for the grand slam but could also have been given a wild card had he proved his fitness.
It is yet another setback for Murray, who turned 34 on Saturday and has played just three tour-level singles matches this year.
He suffered an untimely bout of coronavirus that prevented him travelling to the Australian Open and then picked up the groin injury in his sleep ahead of the Miami Open in March.
Murray’s next tournament is due to be the cinch Championships at Queen’s Club beginning on June 14, although there is an ATP event the previous week in Stuttgart and a second-tier Challenger in Nottingham that he could seek entry to.
Murray headed to Rome last weekend and scheduled practice sessions with several leading players, including Novak Djokovic.
He gained entry into the doubles draw with compatriot Liam Broady as late alternates and played two matches, losing to Kevin Krawietz and Horia Tecau on Thursday.
Murray had appeared positive, saying: “I did pretty well physically for the first points and practice sets at this level for a long time. I was happy with that and hopefully will keep building the next few weeks.”
But, as has become familiar in recent years, Murray’s body has not been able to support his ambitions.