Hollywood producer Arnon Milchan was testifying Sunday at Israeli Prime Minister Benjamin Netanyahu’s corruption trial to answer questions about an alleged “supply line” of champagne and cigars funneled to the Israeli leader and his wife said to have been in exchange for help with Mr. Milchan’s personal and business needs.

Mr. Milchan, who appeared by videoconference from the English city of Brighton, near where he is based, is a key witness whose testimony is essential for prosecutors who are trying to prove that Mr. Netanyahu committed fraud and breach of trust in one of three cases brought against him.

Prosecutors hope Mr. Milchan’s testimony, which extends through this week and next, will paint a picture of plush favors granted to Mr. Netanyahu and his wife that allegedly spurred the Israeli leader to use his position of power to advance Mr. Milchan’s interests. The defense will try to lay out its case that Mr. Netanyahu wasn’t acting in Mr. Milchan’s personal interests and that the gifts were just friendly gestures.

Prosecution and defense lawyers are questioning Mr. Milchan in a hotel conference room in Brighton. While no journalists are allowed to be present there, Mr. Netanyahu’s wife Sara, on a private visit to Britain, will sit in.

Mr. Milchan’s testimony, expected to last six hours, is being aired in a Jerusalem courtroom for judges and other lawyers — who can also ask questions of him — and for journalists and other attendees to watch.

Mr. Netanyahu, who has attended some of the hearings during his trial, arrived at the courtroom shortly after testimony began, flanked by his security detail and aides. Mr. Milchan, who is not charged in the case, greeted him in Hebrew using Mr. Netanyahu’s nickname: “Shalom, Bibi!”

According to the indictment, Mr. Milchan, whose production credits include such hits as “Pretty Woman” and “12 Years a Slave,” gave Mr. Netanyahu and his wife boxes of cigars and crates of champagne over a period of several years that, along with jewelry, amounted to a value of nearly $200,000 — what the indictment describes as a “supply line” of lavish gifts.

The indictment accuses Mr. Netanyahu of using his influential perch to assist Mr. Milchan to secure an American visa extension by drawing on his diplomatic contacts, among them former Secretary of State John Kerry. Prosecutors also accuse Mr. Netanyahu of working to push legislation that would have granted Mr. Milchan millions in tax breaks.

“Considering the many links between the defendant Netanyahu and Milchan, the defendant Netanyahu should have entirely avoided dealing with Milchan’s affairs,” the indictment says, adding that Messrs. Netanyahu and Milchan, an Israeli citizen, have had ties since 1999.

Mr. Milchan is testifying in one of three cases being brought against Mr. Netanyahu. The other two, for which he is charged with bribery, fraud and breach of trust, accuse Mr. Netanyahu of exchanging regulatory favors with powerful media moguls for more positive coverage.

Mr. Netanyahu denies wrongdoing, claiming he is the victim of a witch hunt orchestrated by a liberal media and a biased justice system.

Mr. Netanyahu’s legal woes have dogged him politically and been at the center of a political crisis that sent Israelis to the polls five times in under four years. They also have fueled accusations by critics that Mr. Netanyahu is pushing a contentious government plan to overhaul Israel’s judiciary as a way to escape the charges. Mr. Netanyahu denies those charges.

The trial, which began in 2020 and has still not heard from Mr. Netanyahu himself, has featured more than 40 prosecution witnesses, including some of Mr. Netanyahu’s closest former confidants who turned against the premier.

Witness accounts have shed light not only on the three cases but also disclosed sensational details about Mr. Netanyahu’s character and his family’s reputation for living off the largesse of taxpayers and wealthy supporters. Mr. Milchan’s aide, Hadas Klein, testified last year that the family “loves gifts.”

The idea of a plea bargain has repeatedly surfaced, but prosecutors for now appear determined to see through the trial, despite reports last week that the judges warned them that the more serious crime of bribery will be hard to prove.