Texas said on Thursday that it would drop out of a bipartisan voter integrity group that once included about three dozen states, further destabilizing an organization that has been undermined by right-wing attacks and defections by Republican-led members.

The nonprofit group, the Electronic Registration Information Center, which is known as ERIC and helps maintain accurate voter rolls, confirmed to The New York Times that it had received a resignation letter on Thursday from officials in the nation’s second most populous state.

Alicia Phillips Pierce, an assistant secretary of state and a spokeswoman for the Texas secretary of state’s office, provided The Times with a copy of the letter, which did not give a specific reason for the decision. It will take effect in 91 days.

In response to follow-up questions, Ms. Pierce said in an email that rising membership costs because of declining enrollment had factored into the decision, along with a newly adopted state law that required Texas to pursue alternatives for crosschecking names on voter lists.

“As fewer states participated in ERIC, the costs were set to increase,” she said, indicating that the annual dues would be increasing to $175,000 from about $116,000. “Texas would be paying more for less data.”

Texas is the largest member of the coalition, which has lost Louisiana, Alabama, Florida, Missouri, West Virginia, Ohio and Virginia from its ranks since last year.

The exodus of red states follows intensifying attacks from allies of former President Donald J. Trump, who have falsely claimed that the group is a voter registration vehicle for Democrats and that it received money from George Soros, the liberal billionaire and philanthropist, when it was created in 2012.

This year, Mr. Trump urged all Republican governors to sever ties with the group and claimed without basis in a post on his site, Truth Social, that it “pumps the rolls” for Democrats.

Shane Hamlin, the executive director of ERIC, focused on the group’s future.

“We will continue our work on behalf of our remaining member states in improving the accuracy of America’s voter rolls and increasing access to voter registration for all eligible citizens,” Mr. Hamlin said in a statement.

In June, Gov. Greg Abbott, a Republican, signed a bill that was intended to end the state’s affiliation with the organization.

Bryan Hughes, a Republican state senator who was one of the bill’s sponsors, sowed mistrust about the organization during an online meeting last fall.

“The people that run ERIC are not people who line up with our values, and so we need to have another alternative,” said Mr. Hughes, whose comments were first reported by Votebeat Texas. “Now, there is no evidence that ERIC is doing anything to Texas voter rolls.”

Daniel Griffith, a senior policy director for Secure Democracy USA, a nonpartisan group that promotes secure and fair elections, lamented the move by Texas.

“It’s unfortunate Texas has chosen to withdraw from ERIC without a tested and trusted system to replace it,” he said. “ERIC was created by election officials, for election officials, to ensure accurate and up-to-date voter rolls all across the country.”

He added, “As we head into a presidential election year, building and maintaining confidence in our elections is vitally important, and established, trusted nonpartisan resources like ERIC make that possible.”

Seven states started the organization more than a decade ago. It charges new members a one-time fee of $25,000 and annual dues that are based partly on the population of voting-age citizens in each state. The Pew Charitable Trusts provided seed funding to the group, but that money was separate from donations that it had received from Mr. Soros, according to the website PolitiFact.

California, the nation’s most populous state, is not a member, but a Democratic state lawmaker introduced a bill there this year to enter the state into the group.