In a first direct call for attacks on Twitter, the IS tweets asked "lone wolves" in the US and Europe to make Twitter employees the focus of their attacks, the website Vocativ reported.
"#The_Concept_of_Lone_Wolf_Attacks The time has arrived to respond to Twitter's management by directly attacking their employees and physically assassinating them!! Those who will carry this out are the sleepers cells of death," read an IS tweet.
"#The_Concept_of_Lone_Wolf_Attacks Every Twitter employee in San Francisco in the United States should bear in mind and watch over himself because on his doorstep there might be a lone wolf assassin waiting," another tweet said.
The Twitter handle in question, @dawlamoon, represents Al Nusra Al Maqdisia (The Supporters of Jerusalem) - a Jerusalem-based group that pledged loyalty to IS this year.
Twitter has closed several IS accounts and those of similar terror organisations.
Twitter has also suspended the @dawlamoon account after the threats to its staff were posted, reports added.