"Not tonight!" the US leader protested as Jagger and Blues legends B.B. King and Buddy Guy invited him to sing-along to the classic "Sweet Home Chicago."
To cheers from the audience, a smiling Obama sang parts of the tune, an ode to his adopted hometown, originally made famous by the legendary bluesman Robert Johnson.
Mr Obama singing soul legend Al Green's "Let's Stay Together" was a sure-fire hit last month, garnering positive coverage on cable news and online -- one of the videos of him crooning "I'm so in love with you," at New York's famed Apollo Theater in Harlem, has been viewed over five million times on YouTube.
Earlier Jagger, 68, delivered some bluesy rock in his renowned dancing swagger in the East Room of the US presidential mansion at the "Red, White and Blues" event, singing "I Can't Turn You Lose."
He also let loose "Commit a Crime" with fellow British rocker Jeff Beck.
As president, Barack Obama told the audience, "Some nights when you want to go out and just take a walk, clear your head, or jump into a car just to take a drive, you can't do it. Secret Service won't let you. And that's frustrating.
"But then there are other nights where B.B. King and Mick Jagger come over to your house to play for a concert. So I guess things even out a little bit," he joked.
Mr Obama said at the event that the blues remained a popular and powerful genre.
"This music speaks to something universal. No one goes through life without both joy and pain, triumph and sorrow, the blues gets all of that, sometimes with just a lyric or just one note," he said.
"As we celebrate black history month, the Blues reminds us that we've been through tougher times before."