* Rig drilling relief well at spill site, reconnecting
* Other vessels that left for storm returning
* Upcoming week mostly preparation for static kill
(Recasts, adds detail, quotes)
By Kristen Hays
HOUSTON, July 25 (Reuters) - A rig that had been drilling a relief well to plug BP Plc's (BP.L) (BP.N) Gulf of Mexico oil leak was reconnecting equipment to resume work at the spill site on Sunday, the top official overseeing the spill response said.
Once the last bit of pipe, or casing, is cemented in place near the bottom of the relief well this week, BP will begin a "static kill" the first week of August, retired Coast Guard Admiral Thad Allen told reporters at a briefing.
"Generally the next week will be preps, making sure everything is ready to go," he said.
The leak remains capped after what was Tropical Storm Bonnie disintegrated over the Gulf on Saturday.
Allen had said the static kill, which involves pumping heavy drilling mud and cement into the well from the top, could start three to five days after the casing is cemented in the relief well.
He said on Sunday that the timeline was "refined and revised" after consultations with BP.
The entire operation was interrupted last week when the storm was bearing down on the Gulf.
While most rigs and ships left the spill site out of caution, ships running underwater robots that provide live feeds of the wellhead stayed and continued to operate, BP spokeswoman Jessie Baker said.
Those feeds showed no problems with the cap, which has shut in all flow from the leak since July 15, BP said.
A pair of Transocean Ltd (RIGN.VX) (RIG.N) rigs had been drilling two relief wells, the second well a backup for the first. BP suspended drilling on the second relief well July 13 so it wouldn't interfere with the first one.
BP stopped work on the first well July 20 in advance of the storm and put a plug inside to keep it stable until the last round of casing could be installed.
Allen said on Sunday that the casing work will start "sometime in the next week" once the rig reconnects to the well, removes the plug and cleans out the hole.
While the static kill can start once the casing is in place, the relief well will still bore into the blown-out Macondo well near its bottom 13,000 feet (2.5 miles/4 km) beneath the seabed, Allen said.
Kent Wells, BP's senior vice president of exploration and production, said in an update on BP's website that the static kill might plug the leak on its own. The relief well will confirm that or finish the job, Wells said.
"Those two work in tandem," Wells said.
And Allen said on Sunday that BP will still move ahead with assembling a four-vessel oil-capture system that can handle up to 80,000 barrels a day if needed. (Reporting by Kristen Hays; Editing by Eric Beech)