Musk, the outspoken chief executive of electric car maker Tesla Inc and rocket company SpaceX, advocates developing magnetically levitated hyperloop trains that would travel in airless tunnels, which he says would be more efficient and faster than current high-speed trains.
He recently started a project, the Boring Company, to build transport tunnels.
In tweets on Thursday he said he had "just received verbal government approval for the Boring Company to build an underground NY-Phil-Balt-DC hyperloop. NY-DC in 29 mins" and that the trains would go city center to city center.
Without clarifying, he also tweeted that a first set of tunnels would be to "alleviate greater LA (Los Angeles) urban congestion," adding that the company would "probably" do a loop from Los Angeles to San Francisco, and another in Texas.
"City center to city center in each case, with up to a dozen or more entry/exit elevators in each city," he wrote.
Musk acknowledged there was still a "lot of work" to do before formal approval was granted, but said he was optimistic.
Last month, Musk tweeted that he had "promising conversations" about a tunnel network with Los Angeles Mayor Eric Garcetti.
On its website, the Boring Company says its goal is to lower costs by a factor of 10 or more. Some tunneling projects today cost as much as $1 billion per mile, the company said.
In 2013, Musk said a hyperloop between Los Angeles and San Francisco would cost less than $6 billion and would take 7-10 years for completion.
Major infrastructure projects typically require complex approval from various levels of government and likely would cost billions of dollars.
President Donald Trump in March met with Musk, who raised the Boring Company idea then, White House officials said. Musk also talked about his plans to launch a mission to Mars.
White House National Economic Council Director Gary Cohn in April praised the idea of Musk using tunnels to speed rail transit on the densely populated east coast of the United States and also to cut traffic congestion in Los Angeles.
The White House and Transportation Department did not immediately comment on Musk's tweet. The Boring Company did not immediately respond to a request for comment.