In a statement late on Sunday, Twitter said it was working with law enforcement agencies to see if the Isis' death threats against co-found Jack Dorsey and other Twitter employees were genuine.
Twitter has has been under constant threat from Isis for blocking pro-Isis accounts.
First reported by Buzzfeed, the warning came from a post in a pastebin, which is an anonymous site usually used by programmers for storing computer codes.
"Your virtual war on us will cause a real war on you," read the post on the page which is reportedly based in Poland. Addressed to Twitter founder Jack Dorsey, the post was being circulated by Isis supports, the report noted.
The threat was posted under a logo that includes the image usually seen on Isis black flags, with a mug shot of Dorsey in a crosshairs.
Condemning Twitter's activities to clamp down on any Isis-affiliated account, the post said: "You started this failed war. We told you from the beginning it's not your war, but you didn't get it and kept closing our accounts on Twitter, but we always come back. But when our lions come and take your breath, you will never come back to life."
Quoted by CNBC, Twitter said in a brief statement late on Sunday: "Our security team is investigating the veracity of these threats with relevant law enforcement officials."
It has been Twitter's policy to remove any post or account that spreads Isis' ideologies and operates terrorist propaganda. The policy has angered many supporters of the group, many of whom have posted other warnings and threats to Twitter employees in the past.