WASHINGTON — President Trump’s allegations that former President Barack Obama tapped his phone and his assertions that the bureaucracy is leaking secrets to discredit him are the latest signs of a White House preoccupation with a “deep state” working to thwart the Trump presidency.

The concept of a “deep state” — a shadowy network of agency or military officials who secretly conspire to influence government policy — is more often used to describe countries like Egypt, Turkey and Pakistan, where authoritarian elements band together to undercut democratically elected leaders. But inside the West Wing, Mr. Trump and his inner circle, particularly his chief strategist, Stephen K. Bannon, see the influence of such forces at work within the United States, essentially arguing that their own government is being undermined from within.

It is an extraordinary contention for a sitting president to make. Mr. Trump, who last year angrily dismissed the conclusion of intelligence officials that the Russians interfered in the presidential election to boost his candidacy, has now asked both his staff and a congressional committee investigating Moscow’s influence on the election to turn up evidence that Mr. Obama led an effort to spy on him.

How the White House and its allies see the deep state threat

“What President Trump is discovering is that he has a huge, huge problem underneath him, and I think he’s shocked that the system is as hostile as it is,” said Newt Gingrich, a top adviser to Mr. Trump’s campaign who said he has spoken with Mr. Bannon many times about his suspicion of the deep state and what he sees as its pernicious influence.