Flake told CNN on Tuesday that he voted against a Senate amendment on background checks negotiated by Sens. Joe ManchinJoseph (Joe) ManchinMcConnell: 'Whoever gets to 60 wins' on immigration Manchin: Senators should sign pledge not to campaign against each other  GOP senators turning Trump immigration framework into legislation MORE (D-W.Va.) and Pat Toomey (R-Pa.) because it would have made background checks on gun sales over the Internet too costly.

He said he was willing to change his position if his concerns about Internet sales were met. 

After the CNN report, Flake posted a message on Twitter that underlined his continued opposition to Manchin-Toomey:

Flake's comments come as Democrats seek to hold another vote on the gun legislation. In April, the so-called Manchin-Toomey bill failed to win the 60 votes it needed to pass the Senate. Flake was one of the 46 senators that voted against the bill.

Since voting against the measure, Flake has faced criticism from groups advocating stricter gun laws. A recent poll also found Flake's approval rating at 32 percent. Flake suggested his vote on the background check legislation was largely to blame for the low approval numbers.