WASHINGTON — Two prominent Senate Republicans have drafted legislation that would require President Bush to come up with a plan by mid-October to dramatically narrow the mission of U.S. troops in Iraq.

The legislation, which represents a sharp challenge to Mr. Bush, was put forward Friday by Senators John Warner and Richard Lugar, and it came as the Pentagon acknowledged that a decreasing number of Iraqi army battalions are able to operate independently of American troops.

“Given continuing high levels of violence in Iraq and few manifestations of political compromise among Iraq’s factions, the optimal outcome in Iraq of a unified, pluralist, democratic government that is able to police itself, protect its borders, and achieve economic development is not likely to be achieved in the near future,” the Warner-Lugar proposal said.

Bush has asked Congress to hold off on demanding a change in the course of the war until September, when the top U.S. commander, General David Petraeus, and U.S. Ambassador Ryan Crocker, delivers a fresh assessment of its progress.

Mr. Warner, Republican of Virginia, and Mr. Lugar, Republican Indiana, are well regarded within Congress on defense issues. Mr. Warner was the longtime chairman of the Armed Services Committee before stepping down last year, while Mr. Lugar is the top Republican on the Foreign Relations Committee.

The Warner-Lugar proposal states that “American military and diplomatic strategy in Iraq must adjust to the reality that sectarian factionalism is not likely to abate anytime soon and probably cannot be controlled from the top.”

Accordingly, Messrs. Warner and Lugar say Mr. Bush must draft a plan for American troops that would keep them from “policing the civil strife or sectarian violence in Iraq” and focus them instead on protecting Iraq’s borders, targeting terrorists and defending American assets.

At the Pentagon, meanwhile, Marine General Peter Pace, chairman of the Joint Chiefs of Staff, told reporters that the number of battle-ready Iraqi battalions able to fight on their own has dropped to a half-dozen from 10 in recent months despite heightened American training efforts.

Without providing numbers, the White House had acknowledged in its report to Congress Thursday that not enough progress was being made in training Iraqi security forces — an issue that determines to a large extent when American may be able to reduce its forces there.

Mr. Pace, however, also said the readiness of the Iraqi fighting units was not an issue to be “overly concerned” about because the problem is partly attributable to the fact that the Iraq units are out operating in the field.

Appearing at a news conference with Defense Secretary Robert Gates, Mr. Pace said that “as units operate in the field, they have casualties, they consume vehicles and equipment.”

The Warner-Lugar proposal is the first major legislative challenge to Mr. Bush’s Iraq policy endorsed by the two senators — and lent a more bipartisan imprint to congressional dissatisfaction with the war now in its fifth year.

Earlier this year, both Messrs. Lugar and Warner expressed grave doubts about Mr. Bush’s decision to send 30,000 extra troops to Iraq. But both have been reluctant to back binding legislation that would force the president’s hand.

The legislation would direct Mr. Bush to present the new strategy to Congress by October 16 and suggests it be ready for implementation by December 31.

The proposal also would seek to make Mr. Bush renew the authorization for war that Congress gave him in 2002. Many members contend that authorization — which led to the American invasion of Iraq in 2003 — was limited to approval of deposing dictator Saddam Hussein and searching for weapons of mass destruction.

In still another development Friday, Mr. Bush’s top spokesman appeared resigned to the fact that the Iraqi parliament is going to take August off, even though it has just eight weeks to show progress on military, political and other benchmarks designated by America.

However, Tony Snow said, “Let’s also see what happens because quite often when parliaments do not meet, they are also continuing meetings on the side. And there will be progress, I’m sure on a number of fronts.”

Earlier Friday, Secretary of State Condoleezza Rice exhorted congressional critics to give the administration and the fledgling government until September to “make a coherent judgment of where we are.”

On the morning after the House voted 223-201 for a Democratic proposal to force an American troop withdrawal by next spring, she acknowledged that al-Maliki’s government hasn’t achieved “as much progress as we would like. But we shouldn’t just dismiss as inconsequential the progress that they have made.”

And a top U.S. commander in Iraq, Major General Benjamin R. Mixon, told Pentagon reporters in a separate news conference via video linkup from Iraq that “there will be consequences” if American troops withdraw too soon.

Mr. Mixon spoke of a troop drawdown that would be smaller and slower than Democrats envision.

“It needs to be well thought out,” he said of any plans to drawn down forces. “It cannot be a strategy that is based on ‘Well, we need to leave.’ That’s not a strategy, that’s a withdrawal.”

Congressional Democrats, who have said the war was draining American assets from the fight against Al Qaeda, moved earlier Friday to highlight what they see as a major failure in Mr. Bush’s war on terror: the inability to bring Osama bin Laden to justice.

The Senate voted 87-1 in favor of doubling the reward to $50 million for information leading to his capture. The bill also would require regular classified reports from the administration explaining what steps it’s taking to find Mr. bin Laden.