The Freedom Caucus includes 30 conservative Republican members who successfully blocked a GOP plan to hold a vote last month to repeal and replace the ACA.
The amendment allows states, under certain conditions, to apply for waivers from provisions that ban insurance companies from charging people with pre-existing conditions higher premiums if the state offers high-risk insurance pools as an alternative.
"The MacArthur amendment will grant states the ability to repeal cost driving aspects of Obamacare left in place under the original AHCA," the Freedom Caucus said in a statement.
With the support of the Freedom Caucus, House leadership is close to the 216 votes needed for passage.
The Associated Press reported that House Speaker Paul Ryan said the changes were helping the legislation gain support, but he stopped short of saying the plan has the votes the GOP would need to finally push the high-profile measure through the House.
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