The meeting comes at the end of a week in which Trump's public skepticism over evidence Russia interfered in the US political process has pitted him against the country's top spy chiefs and high profile lawmakers in both parties.
With just two weeks until his inauguration, there are concerns over Trump's seeming refusal to give more credence to the views of leading US intelligence agencies than to those of Russian President Vladimir Putin and WikiLeaks fugitive Julian Assange.
What's been said?
On Thursday, Clapper laid bare both his concerns and those of his colleagues at the President-elect's views of the US intelligence community.
Speaking at a hearing on global cyberthreats that focused almost exclusively on Moscow's alleged hacking during the presidential elections, he said there was a difference between "skepticism and disparagement."
"I do think public trust and confidence in the intelligence community is crucial both in the US and in other countries that rely on US intelligence," he said.
"I've received many expressions of concern from foreign counterparts about the disparagement of the US Intelligence Community, or I should say, what has been interpreted as disparagement of the US intelligence community."
As officials try to make sense of Trump's skepticism, one theory is that the President-elect is concerned that his victory is being undermined by allegations that Russia tried to affect the 2016 vote.
Republican John McCain, the committee chairman, emphasized the Russian role and delivered an implicit rebuke to Trump, who has urged people to "move on" from the issue of Moscow-directed hacking.
"Every American should be alarmed by Russia's attacks on our nation," he said. "There's no escaping the fact that this committee meets today ... in the aftermath of an unprecedented attack on our democracy."
During the hearing -- a rare show of bipartisan unity in Washington -- Democratic Senator Richard Blumenthal said Trump's "demeaning and dismissive" comments about intelligence officers were unacceptable, and praised their service.
On Thursday, US intelligence identified the go-betweens the Russians used to provide stolen emails to WikiLeaks, according to US officials familiar with the classified intelligence report that was presented to President Obama.
The new information has given agencies increased confidence that Russia carried out the hack and did so, in part, to help Trump win.
Included in that new information were intercepted conversations of Russian officials expressing happiness at Trump's win. Another official described some of the messages as congratulatory.
Officials said this was just one of multiple indicators to give them high confidence of both Russian involvement and Russian intentions. Officials reiterated that there is no single intercepted communication that qualifies as a "smoking gun" on Russia's intention to benefit Trump's candidacy or to claim credit for doing so.
What Trump has said
Trump has been prolific on Twitter in recent weeks
, taking on those who have accused him of dismissing the findings of the nation's intelligence agencies.
Last week, Trump suggested that intelligence officials postponed an "'intelligence' briefing on so-called 'Russian hacking'" that they were set to deliver to him this week because they might need more time "to build a case." He called the alleged delay "very strange."
Trump has also faced criticism for appearing to back claims made by WikiLeaks founder Assange, who said Russia wasn't the source of stolen documents from the Democratic National Committee (DNC) that his group distributed.
Trump rejected those accusations, tweeting: "The dishonest media likes saying that I am in agreement with Julian Assange - wrong. I simply state what he states, it is for the people to make up their own minds as to the truth. The media lies to make it look like I am against "Intelligence" when in fact I am a big fan!"
Trump also questioned claims by the Democratic Party that their computer servers had been hacked, adding: "How and why are they so sure about hacking if they never even requested an examination of the computer servers? What is going on?"
Before the election, when 17 US intelligence agencies issued a public statement concluding that Russia orchestrated the hack of the DNC, Trump immediately cast doubt on those conclusions, arguing it was impossible to distinguish between a Russian government operative and "somebody sitting on their bed that weighs 400 pounds."
After Obama placed a series of sanctions on Russia, Trump issued a statement calling for the country to "move on to bigger and better things" and then tweeted praise for Vladimir Putin for not retaliating against the sanctions.
What the Obama administration is saying
Earlier this week, State Department Spokesman John Kirby told CNN that the US administration is "is 100% certain in the role that Russia played" in election-related hacking.
"There's no question" about what Russia did to "sow doubt and confusion, and getting involved through the cyber domain, into our electoral process," he told CNN's Christiane Amanpour.
"And that's not just an assessment by the President or by [Secretary of State John Kerry] or other Cabinet officials. It's an assessment by the entire intelligence community.
Speaking to WMAQ in Chicago Thursday, Obama said it was "important" Trump and the intelligence community work together.
"My hope is that when the President-elect receives his own briefings and is able to examine the intelligence as his team has put together and they see how professional and effective these agencies are, that some of those current tensions will be reduced," Obama said.
"I can speak to my own experience -- it's going to be important to make sure the President and the intelligence communities are both working on the best possible information."
What Russia is saying
Russia has consistently denied it was involved in any type of hacking
or interference in the US election.
Kremlin spokesman Dmitr Peskov told CNN that Moscow is "sick and tired of those irresponsibly blaming everything on our country. If there is a need for an enemy, why not to try someone else?"
"We have suggested cooperation on combating cyberthreats numerous times," Peskov said. "It was rejected."
Aleksey Pushkov, head of the Foreign Affairs Committee in the State Duma, took to Twitter to criticize the US intelligence community.
"When authorities of a country that created more fake news than the rest of the world, blame Russia for doing that, it's clear: it's one more gigantic fake," he wrote.
"Maybe the main battle for Trump won't be China or North Korea or ISIS. It will be with American mass media that continue an information war against him."