TEL AVIV—Israeli police recommended charging Prime Minister Benjamin Netanyahu with bribery and fraud in a corruption probe involving the country’s biggest telecom firm, marking the latest in a swirl of challenges to the embattled leader ahead of elections next year.

The move could result in the indictment of Mr. Netanyahu, one of President Trump’s most stalwart foreign allies and a key partner in his Middle East policy as the White House prepares to roll out a plan for peace between Israel and the Palestinians.