Rahul Gandhi was earlier asked to depose on 2 June but had sought a fresh date as he was out of the country.
His mother and Congress president Sonia Gandhi has been asked to depose before the agency on 8 June.
While Sonia Gandhi tested positive for COVID-19 on 2 June, she maintained that she will appear before the agency as per the summons.
The National Herald Case
The ED had recently registered the case to probe alleged financial irregularities in the party-promoted group Young Indian, which owns the National Herald newspaper.
The ED reportedly wants to record the statements of Sonia and Rahul Gandhi under criminal sections of the Prevention of Money Laundering Act (PMLA).
The summons to the Gandhis come after the probe agency recently questioning Congress leaders Mallikarjun Kharge and Pawan Bansal in relation to the case.
The questioning of the senior Congress leaders and the Gandhis is part of the ED's investigation to understand the share holding pattern, financial transactions and role of the promoters of Young Indian and AJL, officials had said.
The agency registered a fresh case under the criminal provisions of the PMLA after a trial court in Delhi took cognisance of an Income Tax Department probe against Young Indian Pvt Ltd on the basis of a private criminal complaint filed by BJP MP Subramanian Swamy in 2013.
Following the summons, Congress National spokesperson Randeep Surjewala had said that the ED was Prime Minister Narendra Modi's "favourite weapon."
(With inputs from PTI)