Prince William County fully funded budget requests for Tuesday’s election, the Electoral Board said in a statement Thursday, seeking to debunk claims from some Democrats that long lines were intentional to suppress voter turnout.

It remains unknown how an initial request for $350,000 from the county registrar was later retracted, and it’s unclear whether that money could have been used to buy voting machines.

The worst reported case of long lines Tuesday was at Potomac Middle School in Dumfries at the River Oaks precinct, where voters said they had wait times of more than four hours. Democrats have said the Democratic-leaning district with a large minority population might have been targeted.

Supervisor Frank J. Principi (D-Woodbridge) said in an interview at the site Tuesday that the $350,000 request never made it past county staff members to the Board of County Supervisors for a full vote. It was initially presented at a “budget congress,” or meeting of county directors. A more formal request, however, was never made.

Jason Grant, a Prince William spokesman, provided e-mails between county staff members and Registrar Betty Weimer about the request. The e-mails show that staff members told the registrar before the election that if additional costs were incurred, the county would pick up the tab later in the year from reserve funds.

“That is how important we felt . . . getting the election right was,” Grant said in an e-mail. “I don’t know how much more accommodating we could have been.”

Principi said he knows Weimer made the request and is unsure whether county staff members pressured her to retract it.

“I don’t know the answers to those questions, but I’m going to get to the bottom of this,” Principi said. “I am not at all satisfied that we are adequately resourcing our critical unmet needs, including a $350,000 request presented by the county registrar.”

Because the money for the election would be a one-time expense, Weimer was told to ask for the request later in the year, in a process called “carryover,” when supervisors fund those kinds of expenses, Grant said. But in that process, the Electoral Board asked for just $46,000 for additional costs during the presidential election, including overtime and temporary staff.

Weimer referred questions to the Electoral Board. In its statement, the board said: “The responsibility for assuring that there are enough voting machines to handle the number of voters who come to vote lies completely with the Electoral Board.”

The minutes of a February Electoral Board meeting show that the $350,000 was primarily talked about for “staffing, precincts, temporary help and additional costs for voting machine programming.”

Electoral Board member Richard Hendrix said he doesn’t remember all the details about the request or why the board didn’t ask for the $350,000 later in the year. He said the money was not for more voting machines.

Local jurisdictions are generally prohibited from buying additional touchscreen machines because of a 2007 state law intended to address concerns about machines that do not print paper records.

Localities that rely on electronic machines are required to operate at least one machine for every 750 registered voters. Even though the exact numbers are not yet available, the number of voters is likely to be near the ratio that went to Potomac Middle School.

Some localities have adopted a standard beyond the minimum. In Arlington County, for example, there are many more machines: one for every 200 voters. That is the same ratio required in Maryland.

Hendrix said the county has taken other steps that eased waits at the polls, such as electronic poll books that worked well when voters checked in. As the county and state move toward written ballots — which, according to Hendrix, have a minimum standard of one voting booth for every 425 registered voters — Hendrix said he anticipates an easier process in the future. The Electoral Board is still studying why wait times at Potomac were so long.

“I think we’ll have additional voting machines available by the next election,” he said.

Staff writer Ann E. Marimow contributed to this report.