June 26 (Reuters) - A Federal Reserve plan to relax leverage rules could free up $185 billion in capital and unlock nearly $6 trillion in balance sheet capacity for large U.S. global banks covered by Morgan Stanley, the brokerage estimated on Thursday.

The U.S. Fed unveiled a proposal on Wednesday that would overhaul how much capital large global banks must hold against relatively low-risk assets, as part of a bid to boost participation in U.S. Treasury markets.

The plan, approved by a 5-2 Fed vote, marks the first in a possible series of deregulatory moves led by the central bank's new vice chair for supervision, Michelle Bowman.

The proposal would reform the so-called "enhanced supplementary leverage ratio" so that the amount of capital banks must set aside is directly tied to how large a role each firm plays in the global financial system.

"SLR reform is the first of many capital proposals we expect over Michelle Bowman's tenure," Morgan Stanley analysts led by Betsy Graseck wrote in a note, adding that in a positive for banks the Fed chose the rule change with the biggest increase in excess balance sheet capacity.

Fed officials described the changes as a necessary fix to a rule introduced after the 2008 crisis, saying the leverage requirement had grown over time to occasionally limit bank activity, especially as government debt surged in recent years.

"The Fed's proposal to calibrate eSLR should give the banking system meaningful capacity to expand its balance sheet in low-risk assets," analysts at brokerage Barclays said.

"It makes sense for banks to utilize the theoretical leverage capacity as long as the return from investing in low-risk assets/activity is sufficient," they said.

(Reporting by Manya Saini in Bengaluru; Editing by Sriraj Kalluvila)

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