Israeli negotiators headed to Doha on Tuesday

Israel is sending a negotiating team to Doha, Qatar on Tuesday for further discussions on reaching a ceasefire and captive-swap deal in Gaza, the Times of Israel has reported.

This comes of the heels of the release of US-Israeli soldier Edan Alexander on Monday.

Hamas expressed a willingness to keep engaging diplomatically, and said talks can bring about results where the military option cannot. 

For his part, Israeli Prime Minister Benjamin Netanyahu has said that any negotiation will have to take place "under fire" as he continues to pummel Gaza from the air and seal off large parts of the Strip.