Texas Attorney General Ken Paxton continues to show big leads over Sen. John Cornyn, R-Texas, in their Republican Senate primary race.

A poll from Pulse Research has Paxton leading Cornyn 57% to 38%. The poll was conducted by a super PAC supporting Paxton. A previous poll from the Senate Leadership Fund, which backs Cornyn, shows Paxton leading 56% to 40%.

The poll showed Paxton has higher name recognition, 89% to 84%, than Cornyn, who has represented Texas in the upper chamber since 2002 and recently ran for Republican Conference leader.

Paxton has a favorable-unfavorable ratio of 70% to 18%, while Cornyn's is 53% to 30%. Voters who identify as Trump Republicans support Paxton over Cornyn by 44 percentage points, while voters who identify as Reagan Republicans support Cornyn over Paxton by 15 points.

Several GOP operatives had previously expressed concern that Cornyn had no chance of beating Paxton, Punchbowl News reported. Some Republicans are also worried about how Paxton would fare in a general election, Punchbowl said.

Cornyn's campaign had previously said he is confident he can win the primary against Paxton.

"Sen. Cornyn has a 99% voting record with [Donald] Trump as president and continues to be his close legislative ally," said Cornyn's senior adviser, Matt Mackowiak. "When Texas GOP primary voters completely understand the record of both candidates, we are confident we will win."

The poll was conducted June 17-22 by Pulse Research among 806 Republican primary voters. The poll has a margin of error of plus or minus 3.5 percentage points in 95 of 100 cases.