The picture is brightening for American Airlines, a unit of AMR ( AMR).

On Thursday, new CEO Gerard Arpey said business improved during the first two weeks of his tenure because of stronger bookings and lower fuel costs, sending shares of AMR up 3.6% to $6.64. Since April 25, when the world's largest airline worked out a last-minute deal with unions over labor cuts, which included the resignation of former CEO Don Carty, shares have jumped more than 50%.

Arpey's comments came at a breakfast in its Fort Worth, Texas, headquarters, where the CEO told reporters he was hopeful that the $1 billion loss the company racked up in the first quarter "will represent a low point." He added: "the future is uncertain, but the clouds have parted a bit."

One big issue for American, outside of labor issues, will be reducing the amount it needs to pay out in terms of aircraft leases. AMR is attempting to restructure those lease deals and said it was close to reaching terms with lessors, but at the breakfast, Arpey added caution that the company wasn't yet in the clear.

"I'm optimistic that we are going to get to the finish line and hit the target. But we are not there yet," Arpey said.