By Phil Stewart and Sabine Siebold
BRUSSELS (Reuters) -The United States doubled down on Friday on calls for a ceasefire in Gaza and the release of hostages following the death of Hamas' leader Yahya Sinwar, even as Israel and its enemies Hamas and Hezbollah vowed to keep fighting in Gaza and Lebanon.
U.S. Defense Secretary Lloyd Austin said Sinwar's killing by Israeli forces was a major achievement, given his role as the architect of last year's Hamas's cross-border assault on Israel that triggered the conflict.
His death, Austin said, "removes a huge obstacle."
"Sinwar's death also provides an extraordinary opportunity to achieve a lasting ceasefire, to end this awful war, and to rush humanitarian aid into Gaza," Austin told a press conference at NATO headquarters in Brussels.
His comments followed Israeli Prime Minister Benjamin Netanyahu's vow to keep fighting, telling Israelis that the killing provided an opportunity to "stop the axis of evil."
Asked about Netanyahu's remarks and whether Israel was perhaps missing an opportunity, Austin said: "Of course there is (an opportunity) and we would hope we can work together to take advantage of that opportunity."
"Clearly there are opportunities for a change in direction, and we would hope that parties would take advantage of that, both in Gaza and in Lebanon," he said, without directly addressing Netanyahu's remarks.
Austin said the top priority was securing the release of the hostages still being held by Hamas, including Americans.
"They have been through hell, and so have their families," Austin said. "Those who are holding hostages should release them immediately."
Hamas said hostages would only be released with a halt of hostilities in Gaza, an Israeli withdrawal and the release of its prisoners.
Israel's government has rejected several attempts by its main ally the U.S. at brokering ceasefires in both Gaza and Lebanon, pressing on with its wars.
Israel's arch-foe and the militants' main backer Iran also said Sinwar's death would only fuel "the spirit of resistance".