A group of 30 banks and funds representing 40.8% of Greece's €206 billion of outstanding debt said they would take part in the deal.
Other Greek and foreign banks and pension funds have already pledged to accept the offer.
Private sector creditors are being asked to give up almost three quarters of the value of their investments in return for new Greek bonds.
If they do not accept the offer, Greece has threatened to pay them nothing.
A senior Greek finance ministry official told Reuters the government was now optimistic that well over 75% of eligible bonds would be submitted, easily clearing the original minimum threshold it had set for the deal to proceed.
The Greek government is fighting to cut a public debt burden of 160% of gross domestic product (GDP).
The European Union and International Monetary Fund have made a successful bond swap a pre-condition for final approval of the €30 billion euro bailout agreed last month.
The offer expires at 2000 GMT on Thursday.