Press secretary Jen Psaki said the streaming giant’s introduction of content advisory warnings was a “positive step” but that all major platforms needed to be “responsible and vigilant”.
It comes as Spotify faces fallout from scientists and musicians on its platform over its hosting of The Joe Rogan Experience podcast, which has been known to air anti-vaccination views.
The Duke and Duchess of Sussex have also been “expressing concerns” to Spotify about Covid-19 misinformation but say they will continue to work with the platform.
The couple signed a lucrative deal with the streaming giant to host and produce podcasts, estimated to be worth around $25 (£18 million), in late 2020.
On Sunday Spotify boss Daniel Ek issued a statement saying the platform was working to add a content advisory to any podcast episode that includes a discussion about Covid-19.
At a White House press briefing on Monday Ms Psaki was asked about the actions of the streaming giant.
“Our hope is that all major tech platforms - and all major news sources, for that matter - be responsible and be vigilant to ensure the American people have access to accurate information on something as significant as Covid-19,” she said.
“And that certainly includes Spotify.
“So, this disclaimer - it’s a positive step. But we want every platform to continue doing more to call out misinformation while also uplifting accurate information.
“Ultimately…our view is it’s a good step, it’s a positive step, but there’s more that can be done.”
Grammy-winner Nash, 79, became the latest musician to request his music be removed from Spotify in protest of its hosting of Rogan’s content.
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He followed fellow artists Young, Mitchell and Bruce Springsteen guitarist Nils Lofgren who announced their intentions to remove their music from the site last week.
In a statement on Instagram, Nash said: “Having heard the Covid disinformation spread by Joe Rogan on Spotify, I completely agree with and support my friend, Neil Young.”
Following the controversy Rogan has said he will try to “balance out” the opinions expressed on his show.