"We are announcing $11 billion being sent to the states. This to directly support testing", the official said during a briefing.
Funds come from the CARES Act, already approved by Congress and signed into law by US President Donald Trump.
The White House expects the states to submit testing programs with an emphasis on high-risk communities, like nursing homes, the official added.
"States will be providing us within just a couple of weeks a full testing program, where we have asked them to supply their strategy and specific deliverables and goals to test not only those who need a diagnosis because they are sick but also for contact tracing and surveillance of those in the community because we know there is quite a bit of an asymptomatic carriage of this virus", the official said.
Wider testing is viewed as a prerequisite to safely reopen the US economy after the coronavirus-induced lockdowns.
The White House claims that the country is the world leader in testing with around 9 million tests performed as of Monday morning.
The US government had already earmarked about $3 trillion in COVID-19 relief in previous packages, including more than $2.1 trillion in the initial Coronavirus Aid, Relief, and Economic Security (CARES) act. Yet lawmakers are pointing to the new job numbers as evidence more is needed. Last week the Labor Department reported that the US lost more than 20 million jobs in the worst employment report since the Great Depression.
The US is also the world leader in confirmed COVID-19 cases and related deaths. On Monday, the US virus death toll was close to passing the 80,000 mark, according to the US Centres for Disease Control and Prevention.