President Trump's first full day includes prayers and a visit with spies.

Nearly 24 hours after being sworn in as the nation's 45th president, Trump attended a National Prayer Service at Washington National Cathedral before traveling to CIA headquarters "to thank the men and women of the intelligence community," spokesman Sean Spicer said.

Meanwhile, thousands marched in the streets of Washington to protest his presidency and even challenge its legitimacy.

The CIA visit comes after the new president clashed with intelligence officials during the post-election transition over investigations into Russian hacking of Democratic political officials last year.

Intelligence officials said Russia engineered the hacking in an effort to help Trump, while Trump and supporters said other countries could have been involved. He also claimed the intelligence community leaked damaging information on him, including allegations out of Russia. Trump later acknowledged that Russia was behind the hacking, but that it didn't affect the counting of votes.

In other second-day developments:

• The Trump Department of Justice said the president is within his rights to hire son-in-law Jared Kushner as a White House adviser; a DOJ memorandum said a nepotism law passed by Congress does not apply to the executive branch.

• Trump again took to social media, tweeting that "I am honored to serve you, the great American People, as your 45th President of the United States!"

The new chief executive also tweeted praise for Friday's inaugural events (and one news network's coverage of it).

"A fantastic day and evening in Washington D.C.," Trump said. "Thank you to @FoxNews and so many other news outlets for the GREAT reviews of the speech!"

Others criticized Trump's inaugural address, calling it too dark and pessimistic. Citing the specters of crime, poor education, and shuttered factories, the new president told his constituents, "this American carnage stops right here and stops right now."

A New York Times editorial said Trump ignored positive developments in law enforcement and economic opportunity, and that "the new president offered a tortured rewrite of American history — ignoring the injustices of the past as well as the nation’s economic resilience and social achievements in recent decades."

Trump uses his personal Twitter feed for the post, rather than the official @POTUS one.

The new president extolled his Twitter use during one of the inaugural balls Friday night, asking the crowd, "should I keep the Twitter going or not?" When supporters roared their approval, Trump replied, "I think so. You know, the enemies keep saying, 'oh, that’s terrible.' But it’s a way of bypassing dishonest media.”

Trump supporters said the inaugural address gave them hope he will be able to create the conditions for more jobs and better trade agreements with foreign competitors.

Ray Reynolds, a free-lance photographer from Martinsville, Va., and "Super Volunteer" who made the inauguration ceremony his 47th Trump event, said it was like a "rock concert" that renewed the spirit of his supporters. Reynolds described Trump's non-political business background as an asset: "A successful businessman knows how to negotiate the best deals for the best price."

After the speech and an inaugural parade, Trump signed a series of executive orders that included a demand to federal agencies they they work to reduce the "economic burden" of President Obama's health care law, part of the Republicans' effort to "repeal and replace" the law known as Obamacare.

The Trump administration also ordered a regulatory freeze, similar to the ones imposed imposed by presidents Obama and Bush at the start of their terms.

Newly Trump-led agencies and departments are also starting to assert their authority.

On another social media front, The Washington Post reported that the administration ordered the Interior Department to shut down its Twitter account after it opposed unflattering pictures of the size of the crowd at Trump's inaugural, much smaller than the one Obama had in 2009.

“All bureaus and the department have been directed by incoming administration to shut down Twitter platforms immediately until further notice,” said an email obtained by the Post.

Some congressional Democrats continue to assert that Trump's very presidency is illegal because of ongoing business interests; Trump said he has turned over all of his business operations to his sons and other managers, but ethics attorneys said that is not good enough.

Rep. Ted Lieu, D-Calif., said he has begun a "Cloud of Illegitimacy Clock" to time the businessman's ongoing violations of the Constitution.

"While holding office, Mr. Trump will receive — by virtue of his continued interest in the vast and global Trump Organization and his stake in hundreds of other entities — steady stream of monetary and other benefits from foreign powers and their agents," Lieu said. "This is illegal."