MANILA — Through controversy after controversy, President Rodrigo Duterte of the Philippines has always been able to count on his appeal among the nation’s poor. But soaring prices for staples like rice are starting to alienate that vital base of support.

During his presidency, Mr. Duterte has clashed with cherished institutions like the Roman Catholic Church, made jokes about rape and led a brutal war on drugs that has left thousands dead.

But he now faces deepening discontent in an area that particularly affects the urban poor: the price of food.

The country’s inflation rate has hit a nine-year record — 6.7 percent — after climbing for nine consecutive months, the Philippine Statistics Authority said last week. That situation is bad enough that on Tuesday Mr. Duterte ordered restrictions dropped on the importing of rice, ending a decades-old protectionist policy administered by the country’s National Food Authority.