After a Q&A session in the Riksdag, Billström told reporters on Thursday that he had not, despite the uproar, considered resigning at any point in the past few days.
"When you mess up you apologize, get your act together, and shape up in your job," he told the TT news agency.
The furore stems from a newspaper interview on Monday about rejected asylum seekers hiding in Sweden, which contained the blonde comment by Billström that sparked a near immediate backlash.
"Sometimes we have this image that people in hiding live with a nice Swedish lady in her fifties or sixties who wants to help," Billström told DN.
"But that's not how it is. Most of them live with their countrymen who aren't at all blonde and blue-eyed."
Angry reactions were quick to pile up.
Christian Democrat leader and government colleague Göran Hägglund said Billström's choice of words was "inappropriate".
Among the government coalition's opponents, Social Democrat MP and integration policy spokeswoman Ylva Johansson took to Twitter to describe Billström's formulation as "unpleasant and dangerous".
A day later, the prime minister, Fredrik Reinfeldt, joined in the criticism.
"He's made a few mistakes recently," Reinfeldt told the TT news agency.
"Therefore, I've made it clear to Tobias Billström that the way to regain confidence is by holding himself to the humanitarian line we have in our policies."
On Thursday, the beleaguered minister took to the floor of parliament to address the fracas.
"I want to apologize for how I chose to express myself," he said.
"I also want to confirm that I will work hard and be even clearer than before that I am on board the government's line on having a humane asylum policy."