Spicer's comments were made at a press conference following the sudden resignation of National Security Advisor Michael Flynn.
Flynn's troubles have consumed the White House for days. The most unsafe person in the White House still has a job.
Republican Sens. John McCain (R-AZ), Roy Blunt (R-MO), Lindsey Graham (R-SC), Bob Corker (R-TN), Marco Rubio (R-FL), and John Cornyn (R-TX) also expressed support for investigating Flynn's conversations with Kislyak. That was the first story, anyway.
Conway did not say Trump asked for Flynn's resignation. But the real question is the age-old puzzle about corruption in the White House: "What did the president know and when did he know it?".
This official said Flynn "did discuss sanctions".
Ryan said he would leave it up to the White House to discuss "the circumstances that led" to Flynn's ouster, but "the key is this: As soon as the person lost the president's trust, the president asked for his resignation, and that was the right thing to do".
Mr Flynn had only been in the position for three weeks.More news: S Korean investigators to again summon Samsung Heir Jay Y Lee
The president already has questioned the sourcing of media reports, particularly concerning Flynn. "And is there any reason to believe that anybody knew that and didn't take the kind of action they should have taken?" The media seems newly energized by the cascade of leaks from the intelligence agencies.
Pence also said Flynn and Kislyak "did not discuss anything having to do" with the Obama administration's decision in late December to expel dozens of Russian diplomats.The Russians were sent home in response to allegations of Russian cyber-spying against Democratic candidate Hillary Clinton during the 2016 presidential campaign.
Trump on Wednesday took swipes at the intelligence community for "illegally" leaking information to "failing" newspaper outlets.
Flynn, a retired U.S. Army lieutenant general, was an early supporter of Trump and shares his interest in shaking up the establishment in Washington.
The senator said he did not know whether whoever leaked the information broke the law but added: "Leaks of this nature are incredibly damaging to America, to our national security, and we need to look into it".
A transcript of the call produced by the US intelligence community shows that the two men did discuss sanctions, NPR reported.
A bipartisan resolution co-authored last week by Gardner asks the U.S.to "strengthen its commitments" to North Atlantic Treaty Organisation and - in a nod to Trump's criticism - ask that member nations "fulfill their pledge to invest at least 2 percent of gross domestic product on defense spending".