A policy issued Monday would restrict the circumstances in which that subsidy could continue, amid renewed proposals to end it.
The GOP senator had demanded answers for how President Obama's healthcare law would affect Capitol Hill staffers.
Decision addresses issue that has caused anxiety as deadline approaches for some to switch to Affordable Care Act coverage.
A GOP senator says he will delay a vote until getting answers about congressional staffers' health coverage under Affordable Care Act.
The proposal followed rumors that Democrats were trying to exempt members of Congress and their staffs from a requirement to enroll in the exchanges established under ObamaCare.