TORONTO — Prime Minister Justin Trudeau of Canada promised a fresh approach to politics, one that was based on openness, decency and liberalism.

Now he is embroiled in a scandal involving accusations of back-room deal-making and bullying tactics, all to support a Canadian company accused of bribing the Libyan government when it was run by the dictator Muammar el-Qaddafi.

Canadian newspapers are filled with outrage and opposition parties are calling for a resignation. Elections are still seven months away, but some members of Mr. Trudeau’s own governing party fear the scandal has armed opposition parties with rich campaign fodder against its leader, who promised “sunny ways” in politics.

“This is a huge, huge blow to Justin Trudeau’s personal brand and Justin Trudeau’s promise of doing politics differently,” said Shachi Kurl, the executive director of the Angus Reid Institute, a nonprofit polling firm based in Vancouver.