TEL AVIV—Embattled Israeli Prime Minister Benjamin Netanyahu is putting President Trump at the center of his re-election campaign, aiming to leverage close ties with Washington as he faces pressure from political rivals and a possible indictment on corruption charges.

By tying his political fortunes to Mr. Trump, Mr. Netanyahu isn’t only seeking to solidify his base but also to woo undecided voters at a critical juncture of Israel’s election season—and a perilous moment for his tenure as Israel’s prime minister.

Mr....