TEL AVIV, Israel — A senior Qatari official has urged Israel and Hamas to show “more commitment and more seriousness” in cease-fire negotiations in interviews with Israeli media, as pressure builds to reach a deal that would free some Israeli hostages and bring a cease-fire in the nearly seven-month-long war in Gaza.

Qatar, which hosts Hamas headquarters in Doha, has been a key intermediary and was instrumental, along with the U.S. and Egypt, in helping negotiate a brief halt to…