BP Plc may permanently shut the well that caused the worst off-shore oil spill in U.S. history as early as Monday, the company said as speculation grew over assets it might sell to cover mounting costs.

Incoming BP chief executive, Bob Dudley, said on Wednesday the company would stay involved with the cleanup process in the Gulf of Mexico long after the leaking well was plugged and expressed optimism the damaged environment would recover.

It is possible that as early as Monday or Tuesday this well might be killed, Dudley said on National Public Radio.

There's no precision, there's nothing guaranteed. I'm hopeful and I do believe we've seen the end of oil flowing into the Gulf, he added.

A so-called static kill operation that involves pumping drilling mud and cement into the well from the top will be attempted early next week, but a relief well to intercept the ruptured one is seen as the ultimate solution for the leak, which has been temporarily sealed for almost two weeks.

The relief well should be completed by mid-August.

The U.S. government remains cautiously optimistic. The top official overseeing the spill response said on Wednesday he was confident a relief well preceded by the static kill would plug the leak for good.

Retired Coast Guard Admiral Thad Allen would not go so far as saying the next steps are foolproof, but he said at a briefing in New Orleans, We are optimistic that we will get this thing done.

One hundred days after a rig explosion killed 11 workers and opened up an oil-spewing gash on the sea floor, criminal and civil investigations were examining whether BP and other companies involved misled both regulators and investors.

The investigation is ongoing ... there will be a criminal inquiry as well as civil investigation and it involves more than simply BP, U.S. Attorney General Eric Holder said in Cairo.

BP has said the U.S. Justice Department and Securities and Exchange Commission have launched a probe into market trading connected to the spill.

The Washington Post said a BP Squad made up of several government agencies was conducting a criminal probe although it could be more than a year before any charges are filed.

BP also faces a number of private lawsuits and claims for compensation from the spill that damaged fishing areas and tourist sites. The company expects to spend $60 million in advance payments in August, and has already handed out $256 million to those who have lost money because of the spill.

MASSIVE CLEAN-UP

Although the flow of oil has stopped, there is still a massive clean-up operation that experts say will last for months. The major oil slicks appear to have dispersed and experts are analyzing the extent of pollution in the sea.

We're feeling very cautiously optimistic with the well capped and the fact that we're not seeing much oil on the water, Coast Guard Captain Steven Poulin said.

I can tell you there is a lot of blue water out there and just very limited sheening, and very limited patches, I should stress, of emulsified oil. We're not seeing a lot of oil out there that's skimmable at all, he said.

An area of nearly 60,000 square miles (150,000 sq km) of Gulf of Mexico waters is closed to fishing and more than 600 miles of coastline in four U.S. states is affected by oil, according to the latest U.S. government reports.

An environmental advocacy group said on Wednesday it could be years before some Gulf beaches recover fully from the oil spill and are declared free of toxic pollutants.

Because of the spill, there have been nearly 10 times as many beach closing and public health advisories posted this year than there were last year, the Washington-based Natural Resources Defense Council said in a report.

We're not going to rest until we ensure that we've cleaned up all the oil, restored the damage that's happened to the Gulf, and make sure that the people of that region are whole again, White House spokesman Bill Burton said.

While several U.S. agencies investigate the spill, Congress is targeting BP through proposed energy legislation. Lawmakers could lift a cap on total liabilities and impose new safety rules. A bill in the House of Representatives would go one step further by banning BP from getting new offshore oil exploration leases for up to seven years.

Dudley said the proposed bill appeared to be tailored for BP and warned that banning one of the country's largest employers in the Gulf could have unintended consequences at a time of high unemployment, standing now at 9.5 percent.

Democrats were trying to schedule debate on the Senate version, but Republicans and some moderate Democrats voiced opposition, raising doubts about whether there would be enough votes for passage before an August 6 recess.

U.S. Senator Bill Nelson also called for a congressional probe into BP's plan to take a $10 billion tax deduction to help cover more than $30 billion in spill costs.

WHAT'S FOR SALE?

BP's shares ended lower by nearly 1 percent in London and New York on Wednesday.

Sources with direct knowledge of the matter said BP was in talks with India's Reliance Industries and Essar to sell retail assets in Africa with an estimated price tag of $500 million.

Its Indonesian unit rushed to pre-empt speculation its assets there might be for sale.

In Indonesia, there is no change to our strategy and plans. Indonesia is an important area for BP, BP Indonesia president William Lin told Reuters.

Investment bankers said the assets BP could sell include its stake in Alaska's huge Prudhoe Bay oil field and its interest in Pan American Energy in Argentina, as well as smaller assets in Vietnam, Pakistan and Colombia.

The company has lost about 40 percent of its market value since the explosion.

The critical question remains what BP will look like two years from now, analysts at Morgan Stanley said.

Industry executives said it was a good time to sell assets as relative stability in the oil price in the past nine months makes it easier for buyers and sellers to agree terms.

BP agreed to a $7 billion sale of oil and gas fields to Apache Corp last week, which valued the assets at around $19.40 per barrel of oil equivalent.

(Additional reporting by Muklis Ali in Jakarta, Matthew Lynley and Michael Erman in New York, Yasmine Saleh in Cairo, Rachelle Younglai in Louisiana, Patricia Zengerle, Richard Cowan and Philip Barbara in Washington; writing by Tabassum Zakaria, Emily Kaiser and Ed Stoddard; editing by Mohammad Zargham)