Joe Biden has warned "people may die" if his incoming presidential administration continues to be impeded by Donald Trump.
Speaking in Delaware, the president-elect said co-ordination was needed to tackle the coronavirus outbreak.
He called President Trump's refusal to acknowledge he lost the vote, despite calls to do so from both sides, "totally irresponsible".
"This is not a game," former first lady Michelle Obama wrote on social media.
President-elect Biden has 306 votes in the electoral college, surpassing the 270 threshold needed to win.
Yet Mr Trump, a Republican, tweeted on Monday morning: "I won the Election!"
The Trump campaign launched a flurry of legal challenges in the wake of the 3 November vote to contest ballot counts.
The General Services Administration (GSA), the government agency tasked with beginning the transition process for a new president, has yet to recognise Mr Biden and his running mate Kamala Harris as winners, leaving them without access to sensitive government briefings that are normally provided to an incoming administration.
Aides to the Democratic president-elect have said that Mr Trump's refusal to engage in a transition also means Mr Biden's team has been excluded from planning around a vaccination distribution strategy.
In his speech on Monday, Mr Biden said of the stalled transition: "Does anyone understand this? It's about saving lives, for real, this is not hyperbole."
"More people may die if we don't co-ordinate," he added.
Calling nationwide vaccine distribution a "huge, huge undertaking", Mr Biden said that if his team had to wait until 20 January - his presidential inauguration - until they could begin work on the distribution programme, they would be behind by "over a month, month and a half".
Asked if he would encourage state leaders to reinstate stay-at-home orders, the president-elect sidestepped, and instead called on officials to encourage mask-wearing.