"These are incredibly challenging times, with a couple of terrible incidents in a week, and she is leading the country through those incidents and through this difficult time," the spokeswoman told reporters.
She had been asked whether May was confident she was still the right person to lead the country.
Britain has been hit by multiple attacks by extremists and by a devastating fire at a tower block in London that killed 79 people. May's authority was severely weakened when she lost her parliamentary majority in an election on June 8.
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