A spokesperson said: “They said that they need more time to respond to questions we had and we have given them till April 1.”
If the EHRC proceeds with a statutory investigation, it will be able to use its powers to compel the party to reveal details of its handling of antisemitism in recent years, including internal communications such as texts and emails.
It can also seek court injunctions to prevent further antisemitic discrimination and victimisation, and impose an action plan on the party.
Announcing this earlier this month, an EHRC spokesperson said: “We believe Labour may have unlawfully discriminated against people because of their ethnicity and religious beliefs.
"Our concerns are sufficient for us to consider using our statutory enforcement powers. As set out in our enforcement policy, we are now engaging with the Labour Party to give them an opportunity to respond.”
The party said at the time it "completely rejected any suggestion the party has acted unlawfully" over how it handled Jew-hate.
According to a Labour source, the party knew the EHRC was to announce an inquiry for some weeks and has been negotiating terms of reference.
Labour has been approached for comment.