The plans are part of the stress-testing regime meant to determine how the biggest U.S. banks would fare in a financial meltdown.
In March, the Fed said Goldman and JPMorgan could move forward with plans to buy back shares and pay dividends.
But regulators said the stress tests, or Comprehensive Capital Analysis and Review (CCAR), showed both banks had flawed processes for determining capital payouts to shareholders.
Regulators told the two banks to fix the problems and submit new plans by the end of the third quarter.
"We are pleased that the Fed determined that our CCAR process improvements met their expectations," JPMorgan's chief executive, Jamie Dimon, said in a statement on Monday.
The bank, which has come under intense scrutiny by regulators, this year committed some 5,000 people to shoring up an assortment of business controls and processes, including monitoring risk and guarding against money laundering.
Goldman in a statement said the Fed had not objected to its new plan. A spokesman did not immediately have further comment.
Regulators began testing the biggest banks after the 2007-2009 crisis. As part of the tests, banks must submit capital distribution plans for Fed approval.
Regulators can block banks from carrying out those plans if they think buying shares or paying dividends would pose risks to the banks' stability.
The Fed rejected last year's plans by Ally Financial and BB&T. Both banks have since submitted new plans that regulators approved.
Goldman and JPMorgan were allowed to carry out their capital distribution plans, but the Fed reprimanded the banks based on "qualitative" concerns, not questions about their capital ratios.
Regulators did not disclose at the time what weaknesses they spotted in the banks' capital planning.
(Reporting by Emily Stephenson; additional reporting by David Henry; Editing by Leslie Adler)