Djokovic was bidding for his seventh title in the Italian capital as he prepares for the French Open on 28 May.

Seventh seed Rune will play Norwegian fourth seed Casper Ruud in the semi-final.

Djokovic's preparations for the French Open have been disrupted by injury, having missed the recent Madrid Open with an elbow problem and returning to the court in Rome as he looked to build up form and fitness.

The 22-time Grand Slam champion will have the opportunity at Roland Garros to move clear of Rafael Nadal in terms of the most men's major titles of all time.

Following opening wins against Tomas Martin Etcheverry, Grigor Dimitrov and British number one Cameron Norrie, Djokovic was going through the gears in Rome without yet finding his finest form.

There were signs of tension during a tetchy last-16 match against Norrie, before which Djokovic needed treatment for an injury that he was reluctant to discuss afterwards.

Djokovic, who will be replaced as world number one by Spain's Carlos Alcaraz next week, also needed a medical timeout early in the second set against Rune.

While that was perhaps a factor behind his flat performance, the main reason for the defeat was he could not cope with the problems posed by the Dane.

Rune showed why he is being predicted to win some of the sport's biggest prizes, showing confidence in his shot-making to trade blows with Djokovic and also demonstrating his strong mental resilience.

After racing to the opening set in 38 minutes, Rune lost focus in the second set after a line call went against him.

The ruling by umpire Mohamed Lahyani left Rune livid and he lost serve to go 4-2 down but, after teeing up three break points by finishing an extraordinary 34-shot rally with a sublime drop shot, reduced the deficit to 5-4.

Djokovic upped his level again to threaten another break at 0-30 and - after rain forced the players off court for over an hour - secured the set seconds after the restart to level the match.

But Rune refocused at the start of the deciding set, moving a double break up for 3-0 and maintained concentration to serve out for a second straight win over Djokovic.

With Djokovic out and Nadal not playing because of injury, the Rome men's singles final will be the first since 2004 without at least one of the pair involved.

Later on Wednesday, French Open runner-up Ruud, 24, beat Argentine 24th seed Francisco Cerundolo 7-6 (7-5) 6-4 to reach the semi-finals for a second successive year.