Conservative Sen. Mike Lee said Thursday that he isn't ready to support the new version of a Senate health bill.

The Utah Republican's hesitancy comes after Senate GOP leadership inserted a version of an amendment that he and Sen. Ted Cruz, R-Texas, drafted to help insurers bypass Obamacare's insurer mandates into a new version of the bill released Thursday.

Lee said the new bill is different from the version released last month that he opposed, but he said it was "unclear to me whether it has improved."

"I will need time to study the new version and speak with experts about whether it does enough to lower health insurance premiums for middle class families," he said.

Lee and Cruz were pushing an amendment that would let insurers sell plans that don't comply with Obamacare's insurer mandates as long as they sold a plan that does.

The revised bill would create a fund that helps insurers cover people with higher medical costs, but to qualify, insurers have to offer one plan that complies with all of Obamacare's mandates, which include guaranteed coverage for people with pre-existing conditions.

The insurer can then offer cheaper plans that cover fewer benefits.

But a major difference that Lee did not agree to is that the new version of the amendment doesn't allow insurers to waive Obamacare's "single pool" regulation, a Lee spokesman tweeted. Obamacare requires insurers to have a single risk pool for small group and individual markets alike.

The inclusion of a version of the Cruz-Lee amendment was enough to get support from Cruz, who said he would vote yes on a procedural motion to advance the bill in the Senate.