Stars including Jay Leno, Ellen DeGeneres and business tycoon Richard Branson have also called for a boycott of the chain, which owns the Beverly Hills Hotel. But the head of the Dorchester Collection chain said that would be wrong-headed, and only harm hotel staff.
"The actions you take have to be seriously considered because they will effect the livelihoods of these people," Christopher Cowdray told Beverly Hills city lawmakers at a council meeting Tuesday night.
Brunei's all-powerful Sultan Hassanal Bolkiah announced last week that he would push ahead with implementing sharia, despite criticism both at home and internationally.
Late next year, punishments such as death by stoning for offenses including sodomy and adultery will be introduced.
The Beverly Hills City Council passed a resolution Tuesday "condemning the government of Brunei for a series of laws that impose extremely harsh penalties, including death by stoning for homosexuality and adultery."
"This resolution is calling for the (Brunei) government to change their laws or to divest themselves of the Beverly Hills Hotel to separate the fact that our iconic hotel is under their ownership," added Mayor Lili Bosse.
Sultan Hassanal owns the historic Beverly Hills Hotel as well as the Bel-Air Hotel in Los Angeles through his company Dorchester Collection, which also has branches in London, Paris, Milan and Rome.
The city council said they would send the resolution to the State Department asking Washington to "take appropriate action to condemn the Brunei government's policies."
The United States has "relayed our concerns privately to the government of Brunei," State Department spokesman Jen Psaki said Tuesday, but it will not follow a growing boycott of the Sultan's luxury hotel chain.
Beverly Hills' mayor called the new laws "shocking, inhumane."
"They must be met with a strong statement of support for human rights of the people of Brunei," she said.
The Dorchester Collection is reportedly owned by the Brunei Investment Agency, a sovereign wealth fund under the oil-rich sultanate's Ministry of Finance.
The upmarket chain also includes the Bel Air Hotel, which is a few miles from the Beverly Hills Hotel although administratively in Los Angeles, rather than Beverly Hills.
It also includes the Dorchester Hotel in London, Le Meurice and Hotel Plaza Athenee in Paris, Le Richemond in Geneva and the Hotel Eden in Rome.
The sultan's support for sharia law has sparked rare domestic criticism of the fabulously wealthy ruler on the Muslim-majority country's active social media, and international condemnation including from the UN's human rights office.
But the sultan has defended the implementation of the law, meant to shore up Islam and guard the South-East Asian country against outside influences.
On Monday, former US talk show host Leno joined a growing list of celebrities vowing to boycott the luxury hotel chain.
Virgin group founder Richard Branson tweeted at the weekend that Virgin employees would not stay at the hotel chain "until the Sultan abides by basic human rights," the British billionaire wrote.
Others who have called for a boycott include talk show host DeGeneres, British comedian Stephen Fry and TV star Sharon Osbourne.