WASHINGTON — Buoyed by the successful debut of its Falcon 9 rocket June 4, Space Exploration Technologies (SpaceX) Corp. is hoping to persuade NASA to waive one of three planned test flights designed to prove its reusable Dragon capsule can ferry cargo to the international space station.

SpaceX is making its case for condensing the demonstration phase even as it prepares to launch its first full-fledged Dragon spacecraft late this summer.

Under its $278 million Commercial Orbital Transportation Services (COTS) agreement with NASA, the Hawthorne, Calif.-based company is on the hook to complete three increasingly sophisticated demonstration flights of Falcon 9 and Dragon before beginning regular supply runs to the space station next year.

Although the Falcon 9 delivered a model of the Dragon capsule into orbit June 4, the flight was not meant to count as a COTS demonstration.

SpaceX founder and Chief Executive Elon Musk says it makes sense at this point to combine the last two COTS flights into a single demonstration.

“The goal of the program was the demonstration of cargo transport to and from the station. The goal was not three flights,” Musk told Space News in a June 10 interview. “That is a means to an end. But if there is a better means to that end, it makes more sense to go with the better means to that end.”

Under Musk’s proposal, SpaceX’s second COTS flight — a five-day mission during which Dragon would approach within 10 kilometers of the space station and exercise its radio cross-link to demonstrate the ability of the station’s crew to receive telemetry from the capsule and send commands — would be combined with the third and final COTS demo, in which Dragon is supposed to berth to the station for the first time.

Musk says if the modified second flight is unsuccessful, the third demo flight could serve as a backup. But if his plan works, the combined demo would clear the way for SpaceX to begin delivering cargo to the orbiting outpost under a $1.6 billion Commercial Resupply Services contract it signed with NASA in December 2008.

Regardless, Musk says that if he is able to achieve the primary objective of the COTS program, he expects NASA to pay SpaceX for all three flights — valued at $10 million each under an amended COTS agreement the company renegotiated with NASA in early 2008 — regardless of the number of demos flown.

“If we achieve the goal of the program, we should get the full amount of the program,” Musk said, adding that negotiations with NASA are under way.

Valin Thorn, deputy manager of NASA’s Commercial Crew and Cargo Program, said that any decision to eliminate a demo flight will have to wait until SpaceX flies its first COTS demo later this summer.

“It looks like we’ll have our first COTS demo in late August, and depending on how well that goes, we would take into consideration and look at how that might change the rest of the demonstration program,” Thorn said June 11.

Musk said SpaceX continues to review data gathered during Falcon 9’s maiden flight, and that he expects to complete a preliminary report by the end of June.

“But I’m not sure we’re going to release that,” he said. “There’s not much point in releasing something that’s just fodder for our competitors who will stop at nothing to kill us.”

Although the flight went well, it was not flawless.

Musk said he was surprised by a pronounced roll that occurred following startup of the rocket’s upper stage.

“We didn’t expect the roll, but it didn’t affect the insertion vector,” Musk said. “If that had occurred on a COTS flight it wouldn’t have made any difference.”

The loss of the Falcon 9’s spent first stage, which broke up on atmospheric re-entry, was another disappointment for Musk, who had hoped to recover the spent core.

“It was never one of the main mission objectives. It really would have been nice to have, but at the same time no one has ever recovered a liquid booster stage before so it would have been history,” he said. “Unfortunately, there was a microwave tracking radar that was supposed to be tracking the first stage, and instead it locked on the second stage after stage separation. So unfortunately we don’t have much information about why it broke up.”

The first stage was equipped with parachutes to enable an intact water recovery.

Musk said recovering the Falcon 9’s main stage remains a goal, but cautioned it could take “five or six flights before we could recover a stage, maybe more.”

With Falcon 9’s maiden flight behind him, Musk said the company is undergoing the readiness review for the first COTS flight, a five-hour mission meant to show Dragon can complete multiple orbits, transmit telemetry, receive commands, maneuver, re-enter the atmosphere and make a safe water landing and recovery.

In May the company acknowledged a delay in the second COTS flight, previously scheduled for November but now slated for April 2011 at the earliest. Musk attributes the slip in schedule to the extra time needed to design the second Dragon spacecraft to berth with the space station, including the addition of a grapple fixture and the avionics and software that comprise the capsule’s proximity operations and berthing system.

However, Alan Lindenmoyer, manager of NASA’s Commercial Crew and Cargo Program, said in late May that a variety of factors contributed to the five-month delay, including the time, attention and resources the company was putting into ensuring the success of Falcon 9’s maiden flight.

“Putting that much attention on the first flight has used up resources that contribute to delays in the subsequent mission,” he told Space News May 27.

Musk says SpaceX has spent roughly $500 million to date developing Dragon and the Falcon family of rockets, establishing launch facilities on the Kwajalein Atoll and at the Cape, and building a rocket test facility in McGregor, Texas.

He said NASA has funded more than half of the company’s total expenditures since 2006, with $248 million coming from COTS and $101 million from progress payments on the Commercial Resupply Services contract.