The Federal Election Commission is embroiled in an internal dispute over the potential cost of partial public financing of House elections.

The fight, which pits a Democratic commissioner against the Republican chairman, is expected to be aired at an FEC meeting today.

In a memo sent to commission members and staffers, Thomas E. Harris charged that figures presented last leek to the House Administration Committee "were inflated and also rested on various unexpressed assumptions." He asked that a discussion of the testimony be added to the agenda for today's meeting.

Harris disputed the testimony of FEC Chairman Joan Aikens, a Republican, who told the House Administation Committee that partial public financing of House races would cost $35 million to $44 million in 1980. Supporters of public financing, who estimate the cost at $21 million to $30 million, attacked Aikens during her testimony.

Harris said the estimates used to arrive at Aikens' figures included gross receipts from both the primary and general election contributions to condidates. The bill under consideration would cover only general elections.

He said the bill provides that no contributions before Jan. 1 of an election year can be matched with federal funds, but the FEC testimony "includes candidate receipts for both calendar year 1977 and calendar year 1978."

He said the FEC testimony used a 5 percent figure to calculate political action committee and party contributions to the candidate.Since those would not be matchable under the bill, the testimony reduced receipt figures by 5 percent. In fact, Harris memo said, political action committee and party contributions made up "on the average close to 27 percent" of the candidates' gross receipts.

He charged that out-of-state contributions were not deducted, though the bill required 80 percent of contributions to come from within the state.

Harris also said the costs were computed on the assumption that exery eligible candidate would accept public financing, though the bill leaves it up to the candidate as to whether to accept federal money.

The bill before the House Administration Committee would match small contributions up to a $60,000 limit and set an overall spending limit of about $213,000 on what each candidate could spend on a general election.

Aikens is more negative toward the bill than FEC chairmen have been in past years, and congressional supporters of public financing attributed that to the fact that she is a Republican. While some Republicans are cospansoring the bill, the majority of House Republicans oppose the measure.