Kasami joined from Palermo last summer but featured just 17 times for the Whites and made only two appearances in 2012.
The Switzerland Under-21 international was subject of interest from Juventus in January but stayed at Craven Cottage, where he hopes to make an impression next season.
"At the beginning of the season it was quite difficult being in a new team, in a new country, and playing in a new league," he told the club's official website, fulhamfc.com.
"But I felt like I adapted quickly to English football so the first part of the season went very well for me.
"The second half of the season didn't go so well.
"I'm not sad but I'm a little bit disappointed in myself and the only thing I can do is look forward to the next season."