Defense Secretary Mark Esper and Chairman of the Joint Chiefs of Staff General Mark Milley are briefing reporters at the Pentagon on the operation resulting in the killing by special forces of ISIS leader Abu Bakr al-Baghdadi.
The president also suggested he might release some footage of the raid.
The United States and its allies have hailed the killing of Islamic State group chief Abu Bakr al-Baghdadi in a US raid in Syria's Idlib province, announced by US President Donald Trump on Sunday, as a key victory in the worldwide coalition's five-year war against the militant group which once controlled large areas of Syria and Iraq.
Al-Baghdadi detonated a suicide vest that killed himself and three children after he was cornered by U.S forces in a dead-end underground tunnel in his Syrian compound.
Trump said at his news conference that he intentionally had not notified congressional leaders because he was anxious about leaks. "He's a corrupt politician".
Schiff, the Democratic chairing the House intelligence committee, is playing a central role in the impeachment inquiry.
He added: "We all know that".
At another point, Trump mentioned that he was "going to notify" congressional leaders "but we decided not to do that, because Washington leaks like I've never seen before".
Though Baghdadi's death will unsettle Islamic State, it remains capable and unsafe, said Delfin Lorenzana, defense secretary of the Philippines, where the group's influence has taken a hold in its troubled Mindanao region.
British Prime Minister Boris Johnson said: "We will work with our coalition partners to bring an end to the murderous, barbaric activities of Daesh [Arabic acronym for ISIL] once and for all".
Steve Doocy, the host of "Fox & Friends", defended Trump's decision not to inform congressional leaders.
Typically, the White House informs select lawmakers - known as the Gang of Eight - about classified intelligence matters.
When Al-Qaeda leader Osama bin Laden was killed in 2011, the then-House intelligence chair, Republican Mike Rogers, said the Obama administration had kept him apprised of the situation.
House Speaker Nancy Pelosi is demanding the White House provide lawmakers with a briefing on the raid, complaining that the USA notified Russian Federation but kept top congressional Democrats in the dark.
Breakfast Media's Andrew Feinberg accused Trump of wanting to recreate "a we got bin Laden' moment" and said Trump's announcement "should not be carried life, he's forfeited that privilege with all the lying".
Al-Baghdadi had led IS for the last five years, presiding over its ascendancy as it cultivated a reputation for beheadings and attracted tens of thousands of followers to a sprawling and self-styled caliphate in Iraq and Syria.
Since 2014 IS have carefully worked to condition its jihadist fighters and supporters that the group's senior-most figures will be killed, Smith said.
He remained among the few IS commanders still at large despite multiple claims in recent years about his death and even as his so-called caliphate, once the size of Britain, was dramatically whittled away.
"Al-Baghdadi's death is a hard blow against Islamic State, but it is just a stage".