The list of options — laid out in a letter from the chairman of the Joint Chiefs of Staff, Gen. Martin E. Dempsey, to the chairman of the Senate Armed Services Committee, Carl Levin of Michigan — was the first time the military has explicitly described what it sees as the formidable challenge of intervening in the war.
It came as the White House, which has limited its military involvement to supplying the rebels with small arms and other weaponry, has begun implicitly acknowledging that Mr. Assad may not be forced out of power anytime soon.
The options, which range from training opposition troops to conducting airstrikes and enforcing a no-fly zone over Syria, are not new. But General Dempsey provided details about the logistics and the costs of each. He noted that long-range strikes on the Syrian government’s military targets would require “hundreds of aircraft, ships, submarines and other enablers,” and cost “in the billions.”
General Dempsey, the nation’s highest-ranking military officer, provided the unclassified, three-page letter at the request of Mr. Levin, a Democrat, after testifying last week that he believed it was likely that Mr. Assad would be in power a year from now.
On that day, the White House began publicly hedging its bets about Mr. Assad. After saying for nearly two years that Mr. Assad’s days were numbered, the press secretary, Jay Carney, said, “While there are shifts in momentum on the battlefield, Bashar al-Assad, in our view, will never rule all of Syria again.”
Those last four words represent a subtle but significant shift in the White House’s wording: an implicit acknowledgment that after recent gains by the government’s forces against an increasingly chaotic opposition, Mr. Assad now seems likely to cling to power for the foreseeable future, if only over a rump portion of a divided Syria.
That prospect has angered advocates of intervention, including Senator John McCain, Republican of Arizona, who had a testy exchange with General Dempsey when the general testified before the Armed Services Committee about why the administration was not doing more to help the rebels. The plan to supply the rebels with small arms and other weaponry is being run as a covert operation by the Central Intelligence Agency, and General Dempsey made no mention of it in his letter.
On Monday, Representative Mike Rogers, a Michigan Republican who heads the House Intelligence Committee, said that despite “very strong concerns about the strength of the administration’s plans in Syria and its chances for success,” the panel had reached a consensus to move ahead with the White House’s strategy, without specifically mentioning the covert arms program. Senate Intelligence Committee officials said last week that they had reached a similar position.
A Syrian opposition leader said in an e-mail Monday night that with the Congressional reservations largely addressed, American arms would most likely begin flowing to the rebels within a few weeks. “We think August is the date,” the official said.
In an interview, Lakhdar Brahimi, the United Nations special envoy to Syria, expressed disappointment at the Congressional approval. “Arms do not make peace,” he said. “We would like to see the delivery of arms stopped to all sides.”
If ordered by the president, General Dempsey wrote, the military is ready to carry out options that include efforts to train, advise and assist the opposition; conduct limited missile strikes; set up a no-fly zone; establish buffer zones, most likely across the borders with Turkey or Jordan; and take control of Mr. Assad’s chemical weapons stockpile.
“All of these options would likely further the narrow military objective of helping the opposition and placing more pressure on the regime,” General Dempsey wrote. But he added: “Once we take action, we should be prepared for what comes next. Deeper involvement is hard to avoid.”
A decision to use force “is no less than an act of war,” General Dempsey wrote, warning that “we could inadvertently empower extremists or unleash the very chemical weapons we seek to control.”
Mr. Obama has shown no appetite for broad military engagement in Syria, and, if anything, General Dempsey’s letter underscores the president’s reluctance. Some analysts said they believed the administration’s more circumspect public language about Mr. Assad was meant to lay the groundwork for the long-term reality of a divided Syria.
“It’s not a shift, but it’s recognition that the administration’s policy goals will not be achieved during this presidency,” said Andrew J. Tabler, a senior fellow and a Syria expert at the Washington Institute for Near East Policy. “We’re in this for a long slog.”
White House officials said Mr. Carney was not signaling a policy shift or a change in its messaging. But the cumulative effect of comments from civilian and military leaders is unmistakable. “If nothing changes, if we don’t change our game, will he be in power a year from now?” Senator Lindsey Graham, Republican of South Carolina, asked General Dempsey last week, referring to Mr. Assad.
“I think, likely so,” the general said.
In his letter, General Dempsey assessed the risks and benefits of different military options. But his tone was cautionary, suggesting that the Pentagon views all of these options with trepidation.
Training, advising and assisting opposition troops, he wrote, could require anywhere from several hundred to several thousand troops, and cost about $500 million a year. An offensive of limited long-range strikes against Syrian military targets would require hundreds of aircraft and warships and could cost billions of dollars over time. Imposing a no-fly zone would require shooting down government warplanes and destroying airfields and hangars. It would also require hundreds of aircraft. The cost could reach $1 billion a month.
An order to establish buffer zones to protect parts of Turkey or Jordan to provide safe havens for Syrian rebels and a base for delivering humanitarian assistance would require imposing a limited no-fly zone and deploying thousands of American ground forces.
In describing a mission to prevent the use or proliferation of chemical weapons, General Dempsey said the effort would require a no-fly zone as well as a significant campaign of air and missile strikes.
“Thousands of Special Operations forces and other ground forces would be needed to assault and secure critical sites,” he wrote, with costs well over $1 billion a month.

Michael R. Gordon and Eric Schmitt contributed reporting.