* Cap on leak, funneling fraction of oil to drillship

* BP hopes cap will eventually capture 90 pct of oil (Adds comment from CEO, analyst, quotes, detail)

HOUSTON, June 4 (Reuters) - BP Plc.’s containment cap over its stricken Gulf of Mexico well is collecting about 1,000 barrels per day, the top U.S. official overseeing the cleanup effort said on Friday.

A top BP BP.LBP.N executive overseeing containment efforts told CNN earlier that as that collection rate increases, it could corral "90-plus percent" of the oil.

One thousand barrels is a small fraction of the 19,000 barrels per day that the U.S. government has estimated could be gushing from the well, but the amount should decrease as BP closes vents to trap more oil, Coast Guard Admiral Thad Allen told reporters in a conference call.

“Sometime later today we’ll probably be able to get ... an approximation of how much oil we are capturing,” he said. “Generally progress is being made, and I think we need to caution against over-optimism here.”

The containment cap is BP’s latest attempt to trap oil, after its’ “top kill” plan to plug the well failed on Saturday. BP’s strategy is now to trap most of the oil at the well and funnel it to a tanker on the surface until the company finishes drilling two relief wells to plug the leak. Those wells are expected to be finished by mid-August.

Doug Suttles, BP’s chief operating officer of exploration and production, told CNN earlier on Friday that the containment cap “should work.”

“I’d like to see us capture 90-plus percent of this flow,” Suttles said. “I think that’s possible with this design.”

Both Allen and Suttles said BP would continue working to seal the cap on jagged remnants of a pipe on equipment at the wellhead.

“Of course what we have to do is work through the next 24 or 48 hours to optimize that. But that would be the goal ... We want to stop this oil from spilling to the sea,” Suttles said.

Suttles was the first BP official to publicly discuss the cap -- its latest attempt after a series of failures to try to contain the gushing oil and gas leak in the Gulf.

As Allen addressed reporters, BP Chief Executive Tony Hayward sought to reassure investors in a conference call.

“We will halt this spill and put right the damage that has been done,” Hayward said in a statement. “We will rebuild the confidence of the American people and the world in BP.”

BP spent Thursday lowering the cap onto the pipe that had been sheared from the top of equipment at the wellhead.

A rubber seal on the bottom of the cap is intended to capture most of the oil, but some is still expected to escape. (Additional reporting by Chris Baltimore in Houston, editing by Alan Elsner)