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The club have also said that they are working with police in connection with the threatening messages, which were shared online last night.
The threats posted by a Twitter account with the handle @Kieran30971361 made reference to the Manchester Arena bombing in May 2017.
The initial post reads: I wonder how many Portsmouth fans I can shoot everyone remember the Manchester arena bombing just imagine Fratton Park going bang well lets find out tomorrow.
It was then followed by a second threat which said: Bomb bomb fratton park went bang the Portsmouth fans all died. Haha going to be fun tomorrow headline news.
In a statement, the club said: Portsmouth Football Club are aware of a message that has been posted on social media and are working with police on this matter.
The club would like to reassure fans that there will be enhanced security checks in place for Thursdays play-off match against Sunderland at Fratton Park (7.45pm kick-off).
Due to these checks, all supporters with tickets are advised to arrive in plenty of time to make sure they are inside the stadium for the start of the game.
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Police are investigating the matter ahead of the sold-out Sky Bet League One play-off semi-final second leg at Fratton Park