LITTLE ROCK, Ark. — Democratic U.S. Sen. Mark Pryor said Thursday that he will support legislation that would grandfather thousands of Americans' health care plans.

Millions of consumers received health care cancellation notices, and lawmakers in both parties have been pushing such legislation to redeem President Barack Obama's pledge that anyone liking their coverage will be allowed to keep it under the nation's new law.

The legislation that Pryor said he signed onto would oblige insurance companies to continue offering existing paying customers continued coverage under any plans in effect at the end of 2013.

"I've urged the White House to fix this administratively, but until that happens, this is the most reasonable solution," Pryor said in a statement on Thursday.

Pryor, a two-term senator and the lone Democrat in Arkansas' congressional delegation, is running for re-election against Republican U.S. Rep. Tom Cotton next year. Cotton has criticized Pryor for voting for the health care overhaul, and Cotton's campaign was quick to add more criticism on Thursday.

"Recognition by Senator Pryor is long overdue that the disastrous Obamacare law that he played a leading role in crafting is causing great harm to Arkansas families," Cotton campaign manager Justin Brasell said in a statement. "Senator Pryor has voted in partisan lock-step with Harry Reid and President Obama on this issue. He lit the fire and now that it's hurting him politically, he's desperately reaching for the water hose."

Obama invited Pryor and other Senate Democrats facing re-election next year to the White House earlier this week to discuss the problem-plagued health care rollout that could affect their races.

The senators pressed Obama to extend the enrollment deadline for Americans to sign up for health insurance because of the malfunctioning website. Pryor said Wednesday that he told Obama and Biden to "fix the website immediately," address problems with the law and hold accountable those at fault for the mistakes.

"I won't let up until these problems are fixed," Pryor said.