Press secretary Jen Psaki refused to give the ex-president any credit when questioned about it during her daily briefing.
Ms Psaki was asked about recent comments from Admiral Brett Giroir, the former assistant secretary at the Department of Health and Human Services, who has said that the Trump administration deserves more credit for planning the distribution of the vaccine.
“I don’t think anyone deserves credit when half a million people in the country have died of this pandemic,” replied Ms Psaki.
“What our focus is on, and what the president’s focus is on when he came into office just over a month ago, was ensuring that we had enough vaccines – we are going to have them now.”
The Biden White House was critical of the Trump administration’s rollout plans when it took office with the goal of 100 million vaccinations in 100 days.
They are currently on schedule to beat that mark by weeks, and Mr Biden has said that they will have enough vaccine doses for every adult American by the end of May.
Bloomberg statistics show that on 20 January when Mr Biden was inaugurated, the US was administering an average of 900,000 vaccinations a day.
That number has jumped to 2 million doses a day as of 4 March.
More than 28.8 million people have tested positive for Covid-19 and 518,000 have died since the beginning of the pandemic last year.