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New Orleans, Louisiana (CNN) -- One of two relief wells being drilled in an attempt to kill BP's runaway oil well below the Gulf of Mexico is within 20 feet horizontally of it, a company executive said Monday.

The relief well has reached a depth of 16,770 feet, but engineers plan to drill another 900 feet vertically before cutting in sideways, said Kent Wells, BP senior vice president of exploration and production.

"In the last 200 feet, we will angle the well in directly towards it," he said, adding that the drilling, which began May 2, is expected to reach the belching well, known as the Macondo well, in early August.

"While we feel very good about the progress we've made thus far, we've said from day one, roughly 90 days," he told reporters in a conference call. "We continue to think that."

BP has 44,000 barrels of mud ready to inject into the Macondo well in an attempt to end what President Barack Obama has called the nation's worst environmental disaster.

Wells noted that John Wright -- whom he called a world expert -- is in charge of the drilling effort and has been successful in all 40 of his previous efforts to intercept leaking wells.

Asked how many of the 40 wells had been killed, Wells said he did not know. "I don't have the numbers," he said.

But, he added, the chances of killing the well are higher when the interception point is at the bottom of the well.

"We can't guarantee anything, but I think the technology is there," he said. "We've got the best experienced people around, and we're set up to be successful here."

Meanwhile, efforts continue to increase the containment of leaking oil. The next step is to bring in a third rig called the Helix Producer at the well, which would increase the containment by another 20,000 to 25,000 barrels per day, Wells said.

"Basically, we've got about three days of additional work to do," he said. But the work requires a calm sea surface, something that Hurricane Alex, now over the far southwestern part of the Gulf, might not allow.

Although the hurricane is expected to steer clear of the mile-deep hemorrhage, it is still expected to create waves as high as 12 feet in the area, he said. "That will restrict our ability to do these operations" for as much as a week, Wells said.

If the storm's approach were to force the evacuation of the site, "there could be a break of about 14 days to take down the equipment and then bring it back," said Coast Guard Adm. Thad Allen, who is coordinating the federal response to the disaster.

But the state of the sea is not expected to affect subsea containment, Wells said.

As of midnight Sunday, 438,000 barrels of oil and gas had been collected from the Macondo well, he said. That's a rate of about 1,000 barrels per hour, he said.

Researchers have estimated that between 35,000 barrels (about 1.5 million gallons) and 60,000 barrels (about 2.5 million gallons) of oil are gushing into the ocean every day.

The damage emanating from 40 miles off the coast of Louisiana was visible Sunday in Mississippi, where officials reported oily tar balls washing up on their mainland shores for the first time.

"It has hit our shores," said Pascagoula, Mississippi, Mayor Robbie Maxwell. "The good news is that for the last five or six weeks, we've been preparing to attack it when it hit our shores, and that's exactly what we've done."

Mississippi officials said that, while tar balls and "mousse patties" had washed ashore in at least four locations, the areas affected were small and no beaches were closed.

In an effort to combat a less-visible impact of the spill, Louisiana Department of Health and Hospitals Secretary Alan Levine asked Monday that BP pay $10 million to fund six months of mental health services to people affected by the spill.

"There exists anger, anxiety and uncertainty among the families and communities affected by the spill, which will easily manifest into addiction and various forms of mental health crisis if not confronted," he said in a letter to BP Chief Operating Officer Doug Suttles.

Teams have counseled almost 2,000 people in affected areas, and are reporting increases in anxiety, depression, stress, grief, excessive drinking, earlier drinking and suicidal ideation, he said. "These are early warning signs of developing substance abuse and dependence, mental illness, suicide and familial breakdown including divorce, spouse abuse, and child abuse and neglect."

Also, exposure to the oil disaster in the Gulf of Mexico has resulted in 162 cases of illnesses reported to Levine's department, according to a state report released Monday. Of those cases, 128 involved workers on oil rigs or individuals involved in the oil spill cleanup, the report said.

In a separate request, Catholic Charities is seeking $3.2 million for six months of mental health services, he said in the letter, which asked Suttles to respond within a week.

CNN's April Williams, Patty Lane, Chuck Johnston, Brandon Miller, T.J. Holmes contributed to this report.