JERUSALEM — Prime Minister Benjamin Netanyahu of Israel said on Tuesday that he would ask his government to approve naming a new Jewish settlement in the Golan Heights for President Trump, in appreciation of the American leader’s proclamation recognizing Israel’s authority over the long-disputed territory.

Mr. Netanyahu’s announcement, made during a Passover tour of the Golan Heights with his family, came a month after Mr. Trump’s proclamation, which delivered a valuable pre-election gift to Mr. Netanyahu even as it upended decades of American policy in the Middle East.

Despite facing corruption charges, Mr. Netanyahu has since won a fourth consecutive term in office — a fifth over all — setting him on course to become Israel’s longest-serving prime minister, surpassing the record of the founding premier, David Ben Gurion.

“All Israelis were deeply moved when President Trump made his historic decision to recognize Israel’s sovereignty over the Golan Heights,” Mr. Netanyahu said in a video on Tuesday, against the backdrop of the sunny, windswept strategic plateau that Israel captured from Syria during the Six-Day War of 1967.