A pair of three-year-old twin girls and their mother were among 11 Israeli hostages released by Hamas on Monday as a truce between the two sides was extended for another two days.
The latest releases mean Hamas has now released 51 Israelis and 18 foreigners since the ceasefire began on Friday.
Israel released another 33 Palestinian prisoners on Monday from its Ofer prison in the occupied West Bank and from a detention centre in Jerusalem.
It brought the total number of Palestinians it has freed since Friday to 150.
Israel has reportedly been given a list of the additional hostages who could be freed on Tuesday, and has provided its own details of an additional 50 detainees who could be released in exchange.
The two-day extension to the temporary truce between Israel and Hamas will run through Wednesday, and allow for more truckloads of aid to enter the Gaza Strip.