Israel and Hamas have moved closer to agreement on a 30-day ceasefire in Gaza when Israeli hostages and Palestinian prisoners would be released, sources told Reuters, as Israel pressed ahead with its assault on southern Gaza's main city of Khan Younis.

Qatar, the U.S. and Egypt have held shuttle diplomacy since December 28 seeking to bridge differences between Israel and the Palestinian group on a framework for a break in hostilities, which would also allow an increase in humanitarian aid to Gaza.

But the two sides remain at odds over how to permanently end the conflict in Gaza, and Hamas has refused to move forward until this is resolved, the sources said.

The U.S. State Department and White House, Qatar's Foreign Ministry and Egypt's State Information Service did not immediately respond to requests for comment on the Reuters report.

Meanwhile, in its biggest operation in a month, the Israeli military pressed ahead with encircling Khan Younis, where hundreds of thousands of displaced Palestinians are sheltering.

Israeli tanks on Tuesday shut the road from Khan Younis towards the Mediterranean coast, blocking the escape route for civilians trying to reach Rafah on Gaza's southern edge bordering Egypt – now crammed with more than half the enclave's 2.3 million people.

Israeli forces killed more than 100 militants in western Khan Younis in 24 hours, military spokesperson Rear Admiral Daniel Hagari said on Tuesday evening. Israel says it has killed around 9,000 militants in total. Reuters was unable to verify the number.