The images on social media this week showed Chinese fire engines parked at the border, their lights flashing as they waited to be dispatched toward the inferno that was raging eight miles away in northern Hong Kong.

The trucks never entered the city.

On Chinese social media, people questioned why Hong Kong did not take the firefighting help even as its own fire trucks struggled to extinguish the blaze that burned for more than a day and eventually resulted in at least 128 deaths. The moment underscored the delicate political challenge for the city’s Beijing-backed chief executive, John Lee.

Mr. Lee needs to demonstrate that his government, under tighter control by Beijing after a sweeping political overhaul, can manage a crisis of this magnitude on its own. If mainland emergency crews had crossed into Hong Kong, it risked being seen as undermining the city’s promise of running its own affairs.

“People should be sensitive to the image that may arise that the Hong Kong people are unable to deal with matters within Hong Kong,” said Ronny Tong, a senior adviser to Mr. Lee.

Hong Kong said on Thursday that it had not asked for firefighting assistance from the mainland. Mr. Lee said that his government was gradually getting the fire under control and thanked China’s top leader and his boss, Xi Jinping, for his concern.