The 'Tik Tok' hitmaker had been fighting to be released from her recording contract over allegations she was sexually assaulted by the producer, but has now delivered 28 new songs, recorded at her own expense, in order to fulfill her contractual obligations to his label Kemosabe.
Earlier this year, a New York judge denied Kesha's request to be released from her recording contract, and she also lost an appeal in April.
And though she has now dropped her case in Los Angeles, she has filed a similar complaint in New York in a bid to get the ruling about her contract changed.
Her lawyer, Daniel Petrocelli, said: ''Kesha has dismissed her California action without prejudice while she pursues her appeal and other legal claims in the New York courts.
''Kesha is focused on getting back to work and has delivered 28 new songs to the record label.
''We have conveyed to Sony Music and the label Kesha's strong desire to release the single and an album as soon as possible.''
Following the previous ruling, Sony Music - which owns Kemosabe - stated she would be allowed to work with other producers away from Dr. Luke. She subsequently released a track, 'True Colors', with Zedd and recently announced plans to tour.
The 29-year-old singer signed a contract with Luke - who has denied the allegations of abuse - for five albums in 2005 and has so far released just two, with the most recent, 'Warrior', coming out in 2012.
Until she delivered her final three LPs, Kesha could have remained locked in the contract for life.
And now she has delivered the 28 songs, the producer - whose real name is Lukasz Gottwald - may not necessarily release them, if they are not deemed commercially satisfactory.
However, Kesha and her team could provide any failure to make the tracks available as proof Sony and Luke are refusing to release her music.
The 'Die Young' hitmaker recently described the legal battle as ''horrible''.
She said: ''I feel like if you're a human being, you go through pain. And you go through hurt. And every single one of us knows that emotion.
''I don't know if you guys know what I am going through; I'm going through a lawsuit. It's f**king horrible.''
Sony and Dr. Luke have not yet commented on the latest development.
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