Dorsey's remarks, in a series of tweets late Tuesday, came after other major tech companies removed Jones' content for violating hate speech policies.
"We didn't suspend Alex Jones or Infowars yesterday," Dorsey said. "We know that's hard for many but the reason is simple: he hasn't violated our rules. We'll enforce if he does."
Dorsey was responding after Facebook, Apple, YouTube, and Spotify took down material over the past week published by Jones, reflecting more aggressive enforcement of their hate speech policies and raising pressure on Twitter to do the same. Jones's Facebook account has also been suspended for 30 days but he still has a "verified" Twitter account. A separate Twitter account for Infowars is also still running.
"We're going to hold Jones to the same standard we hold to every account, not taking one-off actions to make us feel good in the short term, and adding fuel to new conspiracy theories," Dorsey said.
Dorsey said he wanted Twitter to avoid succumbing to outside pressure but instead impartially enforce straightforward principles "regardless of political viewpoints."
Jones, who has 858,000 followers on Twitter, has built up his profile while promulgating conspiracy theories. His claims include that the 9/11 terror attacks were actually carried out by the government and that the 2012 Sandy Hook mass school shooting, which left 20 children and six adults dead, was a hoax.
Dorsey said that it's the responsibility of journalists to "document, validate, and refute" rumours and sensationalised issues spread by accounts like Jones's so "people can form their own opinions."