The SNP chief said his position was "untenable" following last night's Commons chaos.
The move marks a change in the party's long-standing position on the conflict.
The Labour leader was also savaged by the SNP's Stephen Flynn over the U-turn.
The SNP chief also accused the PM of "taking honesty lessons from Boris Johnson".
The prime minister had just cracked a lame gag about Nicola Sturgeon.
The SNP Westminster leader says Nicola Sturgeon will lead his country out of the United Kingdom.
Stephen Flynn also dubbed Prince Harry's comments about his time in Afghanistan "disgusting".
His victory is a blow for Nicola Sturgeon.