(CNN) Vice President Mike Pence says the latest blockbuster jobs report should prompt the Federal Reserve to consider cutting its benchmark interest rate -- echoing public demands from President Donald Trump on the traditionally independent body.

"This might be a time for us to consider lowering interest rates," Pence said Friday on CNBC following the release of April jobs numbers . "We just don't see any inflation in this economy at all."

Pence was appearing as part of an administration blitz after the Bureau of Labor Statistics reported the US economy added 263,000 jobs in April and the unemployment rate fell to 3.6%, the lowest level since December 1969.

Trump views the strong economy as his best selling point as he prepares to run for reelection in 2020, and has blamed the Fed for hampering him by raising interest rates. A healthy economy has prompted the Fed to raise rates nine times in the past four years, though this week policymakers voted to keep rates unchanged

"We do think that our policy stance is appropriate right now," Fed chairman Jerome Powell, who was appointed by Trump last year, said in a news conference. "We don't see a strong case for moving in either direction."

Earlier this week Trump tweeted the Fed should lower rates by 1% and implement more quantitative easing, moves he said would cause the economy to go "up like a rocket."

"There's no inflation happening here. The economy is roaring," Pence said on CNBC. "This is exactly the time not only to not raise interest rates, but we ought to consider cutting them."

That advice conflicted with comments made later Thursday morning by Kevin Hassett, chair of the White House Council of Economic Advisers.

"I'm not going to give the Fed interest rate advice," he told CNN's Poppy Harlow. "Inflation is under control, and one of the reasons its under control is the global economy is not performing as well as the US economy. There is this risk we could import deflation, and that's something that i think i know that my friends at the Fed are watching closely, that we watch closely as well."

But Trump, who has described Powell as "loco," has been looking to stock the Fed's Board of Governors with supporters who share his economic outlook. So far, he has been stymied by resistance from Republican lawmakers to his out-of-the-box picks.

On Thursday one of those selections, conservative commentator Stephen Moore, withdrew his name from contention after a number of GOP senators said they couldn't support him because of his past writings disparaging women.

Earlier, another pick — the restaurant executive Herman Cain — pulled out when Republicans said they wouldn't vote for him given past allegations of sexual harassment and assault.

Pressed Friday on why two of Trump's picks to sit on the Fed board had failed, Pence demurred, saying only the President is "very interested in bringing fresh ideas to the Federal Reserve board."

That includes people "as fiercely committed to the free market as he is," according to Pence.

As Pence was speaking, White House National Economic Council director Larry Kudlow told reporters that the administration is interviewing candidates to sit on the Fed board.

Asked if the President has more nominees in mind, Kudlow said, "He does."

"No names. We have been interviewing for several weeks, as I've said. And that process will continue," he added.