Bidding for his support for its embattled civil service revision program, the White House told Rep. Herbert E. Harris (D-Va.) yesterday that it is against a District of Columbia tax on the incomes of his suburban constituents.

Harris, who has been antagonistic to the proposed reforms, got the word in a letter from James T. McIntyre Jr.,director of the Office of Management and Budget, that was dated yesterday and delivered by special courier.

". . . The administration would find authorization of a nonresident income tax at this time inappropriate and not consistent with a program of thoroughly exploring alternative methods for balancing revenues and costs of the District," McIntyre wrote.

Harris said he got the letter after being visited earlier this week by William Cable, a White House lobbyist, who was seeking support for the civil service bill.

"I reminded him that I had not gotten an answer to the letter I wrote the president last March asking him to restate his opposition to the commuter tax," Harris said. "He picked up that phone over there, and now I've got this letter."

Carter's position as president is the same as that he took as a candidate in 1976, when his aides managed to block an effort by the D.C. delegation to put a statement of support for a commuter tax into the Democratic Platform.

Mayor Walter E. Washington, who first proposed such a tax in 1971, said he was disappointed by the White House action but had not given up hope.

Despite enthusiastic support from District of Columbia officials and many residents, such a tax has been bitterly fought over the years by suburbanites and their spokesmen in Congress.

McIntyre's letter arrived three days after a House District subcommittee approved legislation by Rep. Ronald V. Dellums (D-Calif.) that would give the D.C. City Council the power to levy such a tax, now prohibited by the city charter.

It would apply to residents of Maryland Virginia who work in the District. If such a tax were enacted, it would add about $200 million a year to the municipal treasury.

The full House District Committee is scheduled to meet at 8.30 a.m. Tuesday to consider the measure.

Even if the bill were approved in the waning weeks of this year's congressional session, any consideration by the Senate is "highly unlikely," Sen. Thomas F. Eagleton (D-Mo.) told a reporter. Eagleton, the chairman of the Senate D.C. subcommittee that would consider the measure, stressed that he favors such a tax.

Dellums, the House bill's sponsor, sharply assailed the White House for its opposition terming it an evidence of colonialism toward a mostly black city.

Dellums said the White House staff as "totally uninformed" in stating that his bill "would authorize a tax" on the commuter income. He said it would merely remove a provision of the city's home rule charter that prohibits such a tax.

Mayor Washington, in letters sent yesterday to all members of the House District Committee, asked for the support of the bill and said flatly that it "would authorize the District of Columbia to tax (nonresident) income earned in the city.

With 61 percent of all income earned in the city now taken to the suburbs, the mayor said, "it is essential to the economic growth of the District of Columbia that the revenue potential of a tax on income earned within the District be made available."

The mayor said the federal payment to the city, which is designed to make up for the city's inability to tax federal property, "is not a base for revenue growth."