CAIRO — Israel and Hamas appear closer than they have been in months to agreeing to a ceasefire that could wind down the 14-month war in Gaza and bring home dozens of people held hostage there. But the sides have come close before, only to have talks collapse over various disagreements . This round of negotiations also faces hurdles.

Secretary of State Antony Blinken said the pressure is on the Palestinian militant group Hamas to move forward with the ceasefire in the Gaza Strip, arguing the group’s support from its allies in the region has dwindled in recent months.

Officials on all sides have cautioned that key details must still be worked out. But there is a general sense of optimism that has been lacking for many months.