(Reuters) - BP shares rose to their highest in nearly a month on Monday, driven by reports of asset disposals to help pay for the company's U.S. oil spill and hopes for a new system to capture almost all the spewing oil.

BP said the cost of the spill was now about $3.5 billion, and that it had collected or flared 749,100 barrels of oil from the well, which ruptured in an explosion in the Gulf of Mexico on April 20 that killed 11 people.

The British oil company is under enormous pressure to halt the oil, which has polluted coastlines on five U.S. Gulf states, threatened multi-billion dollar fishing and tourism industries and killed birds, sea turtles and dolphins.

BP is installing a new capping system that could capture up to 80,000 barrels per day (3.4 million gallons/12.7 million liters), up from about 25,000 bpd. Robots operating a mile under the ocean surface will take up to a week to put the system in place.

BP shares rose 6.9 percent to 390 pence to be the top gainers in Europe, hitting their highest since June 14 and setting them on track for their biggest one-day gain since June 17.