BP PLC's latest attempt to hold back the runaway well in the Gulf of Mexico has succeeded, the company said today.

The "static kill" has successfully pumped enough mud into the wellbore to stanch the flow of oil and gas, the oil giant said in a statement this morning, calling the development "a significant milestone."

Meanwhile, a top Obama administration official said the oil leak is nearly over.

"It's very close in terms of containing the well," Carol Browner, Obama's top energy and climate adviser, said on ABC's "Good Morning America."

"We do feel like this has been an important turning point," Browner added.

The company initiated the static kill yesterday evening after minor leaks had derailed plans to start it earlier. The procedure involves pumping some 84,000 gallons of heavy drilling mud into the wellbore to hold back the flow of oil and force it back into the reservoir.

The company has now entered a monitoring stage. If all goes well, it may begin pumping cement into the top of the wellbore to permanently seal it off within a few days.

But relief well operations will continue. BP insists that the well won't ultimately be sealed off until a relief well intercepts the failed well from the bottom and pumps it and the narrow annulus of space between the wellbore and the surrounding rock with cement.

BP said today that mid-August remains the best estimate of when the first relief well will intercept the failed wellbore to begin kill and cementing operations.

The static kill operations are a supplement to the relief well operations, BP says.

But some offshore drilling experts have raised concerns about the static kill operation.

Art Berman, a geological consultant, wrote late last week on the popular energy blog, "The Oil Drum," that risks are inherent in either a top or bottom kill of the well.

Berman says there are two risks associated with the static kill. One, it may not work at all. It also could rupture the casing of the wellbore by pumping heavy mud under pressure.

Still, he thinks the static kill was a smart move.

"The bottom kill option involves considerably less mechanical risk than the top kill, but time is the enemy, so the top kill makes sense," Berman wrote.

For now, BP says all is well after conducting the eight-hour procedure.