The disturbing messages came after an online debate with Dawn Ennis, a writer and former ABC News assignment editor who, like Manning, is transgender.
Ennis had criticised a message that Manning wrote on May 23, which said in part "voting won't change anything" and called for something "radically different".
It came in a thread in which Manning expressed discouragement over the campaign for US Senate, and general hopelessness that Democrats would retake the House or Senate in November election.
Ennis responded: "When I suggested @xychelsea should consider not running, I stopped short of telling her what to do. But this tweet is just lunacy. Sorry, just cuz you're one of the #girlslikeus you don't get a pass. Tweeting 'voting won't change anything' is wrong and a lie! Just stop. Please."
Manning lives in Bethesda, Maryland and was last seen publicly at a conference in Milan, Italy at the weekend.
The activist in January announced plans to run against incumbent Senate Democrat Ben Cardin.
Manning is a former Army soldier who used to be known as Bradley Manning and was convicted by court-martial in 2013 of violating the Espionage Act for leaking hundreds of thousands of sensitive military and diplomatic documents to WikiLeaks.
Former President Barack Obama commuted the sentence for that conviction and Manning was freed from prison in May last year.
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