Israel ordered 100,000 people in the city of Rafah to flee and took control of the Palestinian side of the crossing with Egypt, closing off aid supplies.
Hopes of a deal have been repeatedly raised and dashed, with differing accounts of what Hamas specifically agreed to.
Polling suggests that while most Israelis prioritise a deal to release hostages over military action in Rafah, that is reversed among the right-wing voters on whom Prime Minister Benjamin Netanyahu's future rests.
The Biden administration is desperate to close a conflict that threatens further regional escalation and is costing it precious domestic support in an election year.
The consequences of airstrikes and the seizure of the crossing by Israel are severe. Humanitarian relief is grotesquely inadequate and famine has taken hold.
Conclusion: Understanding what is happening in Gaza is more essential than ever, as an intensification of the operation threatens to vastly increase the disaster. The cost of failure rises every day.