It would probably cost the District of Columbia about $6 million to $7 million a year to lease the convention center that hardware store executive John W. Hechinger has offered to build in Northeast Washington, a figure that Hechinger touted yesterday as a savings between $1.5 million to $2.5 million over a proposed city-owned facility.

Both Hechinger and city planners agreed in separate interviews that the estimated yearly rental for the convention center would be less than the $8.4 million to $9.6 million debt service the District expects to incur should it win congressional approval to build the center the city has proposed for Mount Vernon Square NW.

"That's a lot of money (saved)," said Hechinger, who on Monday injected a new element into the convention center controversy by annoucing that he is prepared to build a convention facility on property he owns and lease it to the city without charging for the use of the land.

Hechinger reiterated yesterday that by building the convention center on land he owns - an 8.5 acre triangular lot formed by the intersection of Benning Road. Maryland Avenue and 17th Street NE - the District also would save an additional $22 million to $20 million in land acquisition costs now estimated for the Mount Vernon Square site.

The Hechinger proposal got a mixed reception on Capitol Hill, where the city's request for a $27 million loan from the U.S. Treasury to start up the Mount Vernon Square project is pending before a deadlocked Senate-House conference committee trying to reconcile different versions of the D.C. budget for fiscal year 1978.

Rep. William H. Natcher (D-Ky.), chairman of the House District Appropriations Subcommittee and a strong supporter of a city-built and owned center, seemed unmoved by Hechinger's proposal and refused direct comment on it.

Sen. Patrick J. Leahy (D-Vt.), Natcher's counterpart in the Senate and an opponent of such a project, was out of the city. An aide who had spoken to him by telephone said Leahy felt the Hechinger offer doverails with the senator's belief that some private capital should be invested in the center.

City planners said yesterday they were studying the Hechinger offer but still hope the District's Mount Vernon Square proposal will win congress approval. They stressed that the location was part of an entire economic program for the old downtown core and they noted than Natcher previously has disapproved the idea of building a privately finaanced center.

One city aide termed the Hechinger lease offer "not really a lot cheaper" when compared with the advantages of a city-owned facility at what is regarded as a superior site for spin-off development.

Another city planner stressed that the Hechinger proposal is being carefully evaluated. He said Hechinger had visited Municipal Planning Office director Ben Gilbert yesterday to discuss the project.

"The building will cost the same, no matter where it's built," said Hechinger. "But the city will be saving on land coses, and I'm assured by New York lenders that well be able to charge rent that is less than the principal and interest the city will pay if it borrows money to build the center itself."

The location of the center has come a key concern because the city expects to attract revenue-producing hotels retail stores and convention business to offset the cost of the center's construction.

Proponents of the Mount Vernon Square site argue that the downtown area will more easily attract that type of spin-off development. Hechinger has said development can just as easily occur at his Northeast location along the nearby H Street corridor.

Critics of the Hechinger site have said the city will losecontrol of the design and operation of a rented center. But Hechinger said he will "build to suit" and that, as a practical matter, "there will be no difference between owning it or renting it."

At the District Building yesterday, City Council chairman Sterling Tucker complained the Hechinger site "doesn't compare with the area we are recommending. But I don't think it can just be written off either."

Nadine P. Winter, whose ward six would be most affected if the Hechinger site eventually is approved, said she could not very well oppose anything that would "strengthen and revitalize H Street . . . but I don't see where what he's offering is going to do anything for anybody but Hechinger."