Williamson has faced calls, including from some of his own MPs, to quit over the mishandling of schools during the coronavirus pandemic.
He resisted pressure to go following the summer exams fiasco but is again facing calls to quit over the “mishandling” of the impact of Covid-19 on schools, many of which opened for a single day on Monday before being closed again as part of the new lockdown following a government U-turn.
But Allegra Stratton, the PM’s press secretary, stressed that Johnson has full confidence in Williamson.
“The education secretary has been coming forward today with details, plans for people to be educated while not physically in school,” she told reporters.
“So he’s set out a full and comprehensive package for those kids that are not the children of key workers or critical workers who are being educated now at home.
“The PM thinks the package of measures is the right set.”
Stratton added: “It’s a huge brief and the prime minister believes the education secretary is doing it to his utmost of his ability.”
Asked if Williamson was the best person for the job, she replied: “Yes.”
It came as Labour former education minister Lord Knight of Weymouth said Williamson had lost the trust and confidence of parents and teachers.
He told the Lords this summer’s exams were cancelled in Wales in November, allowing time for schools and exam boards to develop “robust alternative assessments”.
Scotland followed suit early in December and “yet ministers in England dogmatically held out until Monday”.
Lord Knight said: “They have catastrophically mishandled the impact of the pandemic on schools.”
Williamson confirmed on Wednesday that GCSE, AS and A-level exams in England this summer will be replaced by school assessments of grades.
He told MPs that the government will put its “trust in teachers, rather than algorithms”, which caused last summer’s exams chaos.