Washington (CNN) -- President Barack Obama met at the White House on Thursday with the families of the 11 workers killed in the BP oil rig explosion.
The president "expressed his condolences and told (the family members) that he, the first lady and the entire administration are behind them and will be there long after the cameras are gone as they go through their unimaginable grief," according to a White House statement.
Obama "also said that while offshore drilling is a part of our nation's overall energy strategy, he simply could not go forward with new deepwater drilling until we have the proper safety measures in place to ensure that a tragedy like this never happens again."
The president was joined by Interior Secretary Ken Salazar, Coast Guard Adm. Thad Allen and White House advisers Carol Browner and Valerie Jarrett.
Several relatives of the victims have expressed opposition to the administration's decision to impose a six-month moratorium on deepwater drilling in order to allow time for an investigation into the April sinking of the Deepwater Horizon rig.
The meeting with the families came as Labor Secretary Hilda Solis headed to Louisiana to meet with fishermen affected by the oil spill and Congress continued with a flood of hearings on what has become an all-consuming issue on Capitol Hill.
White House Press Secretary Robert Gibbs said earlier Thursday that the president also planned "to tell the families he is committed to work with Congress to ensure that any disparity in the law is addressed and the families receive due compensation."
"We are here so that we can be treated fairly," said Shelly Anderson, widow of Deepwater Horizon oil rig worker Jason Anderson. "We want to prevent this from ever happening again."
Sheila Clark, whose husband, Donald, also was killed, says she is "very confident" Obama's going to do "his very best."
Among other things, Democrats are targeting the 1990 Oil Pollution Act, which could limit rig operator BP's liability for economic damages incurred by the Gulf disaster to $75 million. Critics note that the amount is a small fraction of the cost a major oil spill like the Gulf disaster will inflict on communities. BP has said it will waive the cap on damages and pay "all legitimate claims" as a result of the spill, the largest in U.S. history.
In addition, several legislators are seeking to amend the 1920 Death on the High Seas Act, which sharply limits compensation for wrongful deaths on vessels more than three miles from shore.
They've also criticized an 1851 law limiting shipowners' post-accident liability to the value of a sunken vessel. Rig owner Transocean used the law in the days immediately after the April 20 Gulf explosion to attempt to limit its liability to $26 million.
Transocean's attempted use of the 1851 law "is ridiculous," Sen. Chuck Schumer, D-New York, said Thursday. Schumer noted that the statute -- enacted before the rise of the oil industry -- was intended to help bolster the pre-Civil War U.S. shipping industry.
"We can't bring their loved ones back, but we can at least make sure that this terrible tragedy is not compounded" by the law, added Sen. Patrick Leahy, D-Vermont.
Some Republican critics of the effort to remove the liability caps contend that doing so could lead to the creation of an energy monopoly while increasing America's dependence on oil imports.