Hamas is open to "indirect and rapid" negotiations on a prisoner exchange following its bloody military escalation with Israel in May, the Islamist military group said Monday.

"There is now a real opportunity to move this file forward,"  Yahya Sinwar said in response to an AFP query on a potential prisoner exchange.

"We are ready for indirect, urgent and rapid negotiations to conclude the case."

The head of Hamas' political wing in the Gaza Strip -- a Palestinian enclave home to some two million people -- delivered the statement on the sidelines of a visit by Egyptian intelligence chief Abbas Kamel.

Kamel is working to solidify the ceasefire Cairo brokered between Israel and Hamas that went into effect on May 21, after 11 days of Palestinian militant rocket fire and Israeli air strikes.

The aerial bombardments on Gaza killed 254 Palestinians, including 66 children, health officials said. 

Rockets and other fire from Gaza claimed 12 lives in Israel, including one child and an Arab-Israeli teenager, medics said. 

A Hamas official, who requested anonymity, said the Gaza talks focused on three points: turning the ceasefire into a longer-term truce, a prisoner exchange, and the reconstruction of Gaza. 

Sinwar said Hamas had "no objection" to talks on reconstruction and an end to Israel's decade-long siege of Gaza "moving forward in parallel" with negotiations on a prisoner exchange.

"However, we categorically reject any link between these two aspects," he added, without specifying how many prisoners could be released.

In Cairo on Sunday, Israeli foreign minister Gabi Ashkenazi raised the issue of two soldiers thought to be dead and two other Israelis believed to be detained in Gaza.

Since Israel's 2014 invasion of the Gaza Strip, the Islamist group has held the bodies of Israeli soldiers Oron Shaul and Hadar Goldin, although Hamas has never confirmed their deaths. 

Hamas is also believed to be holding two Israeli citizens who entered Gaza alone and whose families say they have mental health issues. 

Israel is meanwhile holding more than 5,000 Palestinians in its jails.

The latest conflict erupted on May 10 when Hamas sent volleys of rocket fire towards Israel in solidarity with hundreds of Palestinians injured in clashes with Israeli security forces inside Al-Aqsa mosque compound.

From May 10 to May 21 the Gaza Strip suffered extensive damage, and international aid has started to pour in. 

Egypt and Qatar each pledged $500 million (about 410 million Euros) for reconstruction.