Malloy charged that the decision by a foundation managing $11.5 million in donations to rely on community members to distribute the money "has unintentionally made the process more difficult, especially on those most directly affected," The Hartford Courant reported Sunday.
"I remain deeply frustrated at both the pace and manner" with the foundation had made decisions about distributing the money, the governor said in a letter to the organization.
The Newtown-Sandy Hook Community Foundation Inc. has said $7.7 million in contributions will go directly to 40 affected families.
Those families would not be eligible to receive any additional money from the fund.
The rest of the money would go into another fund for long-term assistance to the community.
A third party should be brought in to oversee the rest of the money once the $7.7 million is distributed, the governor told the foundation.
"In addition, I would hope that those who have already received donations not be precluded from receiving additional funds," Malloy added.
Family members have been critical of the foundation's process and questioned how it can continue to raise money without any of the additional donations going to the affected families.
The United Way, which oversees the money, maintains the fund was never meant to be a victims' compensation fund.
Martin Bashir resigns from MSNBC over Sarah Palin comments
Gal Gadot cast as Wonder Woman for 'Batman vs. Superman'