The move affects holders of 28.5bn euros ($37.4bn; £23.6bn) of Greek government bonds.
Athens says it will now accept a take-up rate of 72%, or 20.3bn euros' worth of the debt, on 11 April.
Greece is using bond swaps to reduce its debt, with bondholders being asked to accept new bonds that offer lower returns over a longer period.
The latest debt swap applies to bonds issued under foreign law or by state enterprises.
Last month, Greece got backing for its much larger swap of about 177bn euros of domestic law bonds.