House GOP leaders unveiled the measure, which will be an amendment to a temporary government funding bill, on Monday.
President Obama has asked lawmakers to approve so-called Title X authority, to allow the Pentagon to equip vetted Syrian groups.
McCarthy said that the House could hold a vote after the midterm elections on a broader authorization for military force against ISIS.
The House Rules Committee is slated to meet Monday evening on the continuing resolution and the Title X authority.
The measure places clear limits on the administration’s authority.
It requires Defense Secretary Chuck Hagel to submit the administration's plan for training and equipping the rebels 15 days before any activities begin.
Hagel would also have to submit an update to lawmakers every 90 days on how many troops have been trained and deployed, how effective they are on the battlefield, and account for the equipment provided to them.
The Pentagon would be required to list every individual they are recruiting, information on their backgrounds and any possible links to terrorist organizations, according to an Armed Services committee aide.
The bill would not exclude rebels with links to terrorist groups from participating in the program, since that would make it difficult to recruit trainees, the aide said.
The aide said the rebels would likely receive small arms, rocket-propelled grenades and communications equipment.
The amendment was geared towards addressing concerns from both Republicans and Democrats that weapons provided to the rebel groups could fall into the hands of ISIS.
But some lawmakers have expressed opposition even to arming vetted groups.
Sen. Rand Paul (R-Ky.) called the plan "a mistake" early Monday before the measure was released.
"It’s a mistake to arm them. Most of the arms we’ve given to the so-called moderate rebels have wound up in the hands of ISIS, because ISIS simply takes it from them, or it’s given to them, or we mistakenly actually give it to some of the radicals," Paul said on CBS “This Morning.”
Pentagon lays out Syria objectives: The administration so far has publicly shared few details on the $500 million plan to train and equip.
The Pentagon has said it would initially train "more than 5,000" rebels in Saudi Arabia over a year.
On Monday, it laid out three objectives for the program.
One objective is to "to hold and defend liberated territories from ISIL," Pentagon spokesman Army Col. Steve Warren said, using an alternative name for the terror group.
The second objective is “to increase pressure on ISIL as well as the regime” of Syrian President Bashar Assad.
"We've said from the very beginning that the Assad regime has perpetrated horrendous acts against its own population. The moderate opposition was formed as you know in an effort overthrow the Assad regime," Warren said.
The third objective is to possibly carry out “some specific counter-terror operations," he said.
The spokesman did not detail exactly who would be training the Syrian forces, what type of instruction they would receive, or who would lead the rebels after their training.
The Pentagon said it would not start training until Congress approves the authority, which could come this as early as this week.
Hagel, Dempsey head to Congress: Obama administration officials will also be taking their plan to Congress to rally support from lawmakers.
Defense Secretary Chuck Hagel and Chairman of the Joint Chiefs of Staff Gen. Martin Dempsey will testify this week to the Senate and House Armed Services Committees on the president's plan.
Dempsey warned the committee in a letter last year that training and equipping the rebels included the risk of "extremists gaining access to additional capabilities, and insider attacks or inadvertent association with war crimes due to vetting difficulties."
NATO commander calls for Russia 'reset': Supreme Allied Commander Gen. Philip Breedlove on Monday called for a reset of the NATO alliance — one that assumes Russia is not a partner.
"For the last 12 years, we've been trying to make Russia a partner. We've been making basing decisions, force structure decisions, economic decisions, along the fact that Russia would be a constructive part of the future of Europe," he said Monday.
"And now we see a very different situation, and we have to address that," he added, speaking at the Atlantic Council in Washington.
Breedlove is planning to brief reporters at the Pentagon on Tuesday, on his plans to stage more U.S. forces in the region to prevent any future incursions by Russia into other Eastern European or NATO nations.
On Monday, Breedlove discussed his plans to create a NATO reaction force in Eastern Europe, as well as to create a headquarters in Europe dedicated to protecting NATO allies.
Ukrainian president Petro Poroshenko is due to address a joint session of Congress on Thursday, and meet with President Obama later in the day.
Poroshenko hopes to extract concrete pledges of support, either military or financial, from the U.S., as a shaky cease-fire remains in place between Kiev and pro-Russian separatists in eastern Ukraine.
No Obama meeting with Putin, Rouhani: Obama is not expected to meet with Russian President Vladmir Putin or Iranian President Hassan Rouhani at the United Nations General Assembly in New York next week, the White House says.
At last year's session, the White House said the president was willing to meet informally with Rouhani as the U.S. pushed Tehran to begin talks over its nuclear weapons program.
White House press secretary Josh Earnest said "the historical significance of a conversation this year would be somewhat different."
Similarly, Obama is not planning to meet with Putin.
Last week, the administration announced a new round of sanctions targeting Moscow over its incursions into Ukraine.
The U.S. has also been frustrated by the Kremlin's support for Syrian President Bashar Assad, as well as the decision to grant asylum to National Security Agency leaker Edward Snowden.
However, the White House left open the possibility of a meeting, and said there was room for cooperation on ISIS.
"It could be added to the schedule. But I don't have anything like that to announce at this point," Earnest said.
In Case You Missed It:
-Dem Rep. Schiff to offer use-of-force resolution on Syria
-Arab nations offer air support in ISIS fight
-Iran: US planning a war 'to dominate the region'
-Rand Paul: 'Mistake to arm' Syrian rebels
-Putin, Rouhani not on Obama's UN dance card