D.C. Mayor Marion Barry asked the City Council yesterday to delay the city's 2-cent gasoline tax increase scheduled to go into effect June 1. Some service station owners have complained that the increase, which would put the tax at 12 cents a gallon, would drive many of them out of business.

In a letter to City Council Finance and Revenue Chairman John Wilson (D-Ward 1), Barry said that the tax increase should be delayed by one month while city officials assess its impact on Washington service stations.

Vic Rasheed, executive director of the Greater Washington-Baltimore Service Station Association, which represents the city's gasoline station owners, said that the long-scheduled tax increase would have an adverse impact on many businesses because gasoline demand is lower now than it was last year, and because there is a glut of gasoline on the market. Rasheed's organization last year lobbied successfully for the repeal of Barry's ill-fated 6 percent tax on gasoline imposed last August and wiped from the books in November.

This latest tax increase was imposed to replace that 6 percent tax, which would have added about 8 cents to the cost of a gallon of gasoline.

But yesterday Wilson showed no sign of wanting to delay the 2-cent increase. "Nobody went out of business last time, nobody will go out this time," Wilson said. "The problem is that we can't run the city without tax revenues."

Asked about the possibility that some stations might go out of business, Wilson said, "There are casualties in capitalism. You see them every day."

The 2 cents per gallon increase is expected to add $300,000 to the city's budget for the remainder of this fiscal year and $2 million in the fiscal year that begins in October. While Barry wants a 30-day delay, the dealers want a delay until January 1981, and then only a 1-cent increase.