Hamas fighters on Saturday released a second group of 13 Israeli hostages in exchange for Palestinian prisoners, freeing for the first time one of the people snatched during their bloody assault on a music festival.

The hostage-for-prisoner exchange had been delayed for hours in a heart-stopping development when Hamas accused Israel of breaching its side of the agreement, struck as part of a four-day ceasefire that is already past its mid-point.

But after the intervention of Qatari and Egyptian mediators and reassurances from Israel, Hamas agreed to proceed, releasing 13 Israelis and four Thai hostages in a late-night operation.

Israel in turn freed 39 Palestinian prisoners, officials said.

Red Cross mini buses could be seen ferrying the hostages late at night through Gaza's Rafah border crossing with Egypt ahead of their transfer to Israel, AFP photo and video images showed.

Among the freed Israelis was 21-year-old Maya Regev, kidnapped by Hamas in their deadly 7 October assault on the Supernova desert rave, according to a forum of the hostages' families.

Maya Regev and her 18-year-old brother Itay, who was also snatched by Hamas during the festival, were later shown tied up in the back of a pick-up truck in a video posted on social media.

"I am so excited and happy that Maya is on her way to us now. Nonetheless, my heart is split because my son Itay is still in Hamas captivity in Gaza," her mother Mirit said in a statement released by the hostage families' forum.

The family of freed nine-year-old hostage Emily Hand said they were "overjoyed" to embrace her again.

"We can't find the words to describe our emotions after 50 challenging and complicated days," they said in a statement via the forum.

Prison authorities in Israel said they in turn released 39 Palestinian detainees including 38-year-old Israa Jaabis, sentenced to 11 years in jail for detonating a gas cylinder at a checkpoint in 2015.

The handover of Hamas hostages came hours later than expected after the militant group said Israel was interfering in the selection of prisoners for release and was not allowing aid to reach civilians in northern Gaza.