"I have decided to withdraw from the case for personal reasons," Salem al-Hashash told a news conference lasting just a few minutes.
He provided no further details and refused to answer questions.
Jassem Emwazi, the father of Mohammed Emwazi who is thought to be the knife-wielding IS executioner, hired Hashash last week to file cases against those allegedly spreading false rumours about his son and the family.
Reading from a written statement, Hashash said that he filed several lawsuits on Sunday against unspecified parties for slander against his client.
In the statement, the lawyer said Jassem Emwazi is a "British national who has no relation with Kuwait" except that he visits the Gulf state to see his mother.
Hashash reiterated that "so far, Western security agencies have not provided any evidence to prove that Mohammed Emwazi is Jihadi John", who is accused of killing several Western hostages.
He said that the stories and rumours published about him are "untrue and baseless".
Hashash did not say what will happen to the lawsuits he has filed now that he has withdrawn from the case.
Last week, he told Kuwaiti daily Al-Qabas that his client was interrogated by the interior ministry for three hours before being released.
Alleged executioner Mohammed Emwazi was born in Kuwait to a stateless family of Iraqi origin. His parents moved to Britain in 1993 after their hopes of obtaining Kuwaiti citizenship were quashed.
Emwazi visited Kuwait several times, the last time between January 18 and April 26, 2010, Al-Qabas said.
A year later, he was denied entry to Kuwait after his name came up during investigations into attacks in Britain.