In a show of hands, members of parliament overwhelmingly voted for the resolution during a plenary session in Strasbourg, France.
The resolution is not legally binding, but amounts to political pressure.
Blatter, 79, tendered his resignation on June 2 in the midst of a massive corruption scandal, but it will not take effect until December at the earliest.
In the text approved by parliament, legislators welcomed Blatter's resignation, which came just four days after he was re-elected as head of FIFA for a fifth term.
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Since that might not happen for another nine months under FIFA rules, the draft "therefore calls on FIFA to select, in a transparent and inclusive way, an appropriate interim leader to replace Joseph Blatter forthwith," it added.
FIFA's image is in shreds now with around 14 current or former officials and sports marketing executives accused by US prosecutors of taking part in a kickbacks scheme going back 20 years involving a total of $150 million in bribes.