The bill, the Offshore Production and Safety Act, would require lease sales in the Gulf of Mexico, the mid-Atlantic and Alaska, but it would also require drillers to have safety plans in place in the wake of last year's Deepwater Horizon spill.

"We all remember and we shouldn't forget what happened last summer, and we're committed to improving the safety of offshore-permitting activities so that it doesn't happen again," she said.

The bill would also establish timelines for accepting or rejecting drilling permit applications that the Department of the Interior would have to follow, a response to what Republicans say has been ongoing permitting delays under the Obama administration.

As part of her effort to win support for the bill, Murkowski today sought to reach out to Democrats and praised the Obama administration for agreeing to hold lease sales in Alaska, establish a permitting office in Alaska and for exploring permitting in the mid-Atlantic.

"I have routinely criticized this administration on certain aspects of their energy policy," Murkowski said. "But the president deserves credit for taking these steps, and I acknowledge that."

The Senate is expected to vote on the bill, S. 953, at 2:30 p.m.