President Barack Obama did not personally approve Beyonce and Jay-Z's trip to Cuba, the White House said Thursday, after the US rapper released a single online slamming criticism of their travels.

In "Open Letter," Jay-Z -- who with Beyonce worked to raise funds for Obama's re-election campaign last year -- boasts: "I done turned Havana into Atlanta... Boy from the hood, I got White House clearance."

The rapper also slams US politicians who criticized the couple's trip to Havana, saying: "They wanna give me jail time and a fine. Fine, let me commit a real crime... Hear the freedom in my speech."

He continues: "Obama said, 'Chill, you gonna get me impeached'."

When asked about the lyrics, White House spokesman Jay Carney joked: "I guess nothing rhymes with Treasury" -- a reference to the fact that the US Treasury issues clearance for US nationals to travel to Communist-ruled Cuba.

"It's a song," Carney said. "The president did not communicate with Jay-Z over this trip."

After pictures surfaced of the music power couple touring Old Havana last week, Republican lawmakers Ileana Ros-Lehtinen and Mario Diaz-Balart of Florida requested information about the type of permit they received before traveling.

A Treasury official said Beyonce and Jay-Z had gone to Cuba as part of a cultural exchange that did not violate the US economic embargo on the island.

Under the embargo established in 1962, US citizens cannot go to Cuba and spend money without permission from the government.