Sen. Thomas Eagleton (D-Mo.) launched an intensive lobbying effort this week to persuade the Senate to kill language in a D.C. spending bill that would prevent Washington's new Convention Center from booking sporting events, concerts and circuses.

Eagleton, a ranking member of the Appropriations and Governmental Affairs Committees, has circulated a "Dear Colleague" letter and a detailed staff memorandum arguing that the proposed restrictions would encroach on home rule and would run counter to the intent of Congress and the D.C. government in approving the $98.7 million convention center project, which is due to open in January.

The House struck similar language from its version of the $1.9 billion D.C. appropriations bill Sept. 30, just before Congress began a lengthy election recess. At Eagleton's insistence, the Senate postponed action on the controversial measure until after the recess.

Eagleton plans to ask the Senate to strike the restrictive language when the bill is brought to the floor, possibly as early as today, according to an aide. He will encounter stiff opposition from several highly influential members, including Sens. Alphonse M. D'Amato (R-N.Y.), Patrick J. Leahy (D-Vt.) and Paul Sarbanes (D-Md.).

D'Amato is chairman of the subcommittee on D.C. appropriations, which holds the District's purse strings and which approved the restrictive convention center language. Leahy is the subcommittee's ranking minority member.

Former senator William D. Hathaway (D-Maine), a lawyer with the Washington firm of Patton Boggs & Blow, informed Eagleton's office yesterday that he is representing the Capital Centre in the convention center matter. Capital Centre owner Abe Pollin and Maryland officials had sought the proposed restrictions.

"I do not feel that Congress should in any way restrict the Washington Convention Center," Eagleton said in the letter, which was cosigned by Sen. Warren Rudman (R-N.H.), another appropriations committee member. "Such an infringement on the City's home rule is philosophically unacceptable, as well as economically unjustified."

The 12-page staff memorandum suggested that the proposed restrictions would hurt Washington's efforts to compete with other government-owned convention centers for business.

Of the 21 publicly owned convention centers that were surveyed by Senate staff members in preparing the memorandum, including facilities in New York, Chicago, Philadelphia, Detroit, Houston and Los Angeles, none has restrictions comparable to those suggested for the D.C. center.

"All persons surveyed emphasized the keenly competitive nature of the convention center business, many commenting that restrictions of any kind would be disastrous," the memorandum stated.

Proponents of the restrictions contend that in approving the project, Congress assumed that the new convention center would be limited to booking conventions and trade shows, and would not compete with existing facilities for sporting events and rock concerts.

The operating costs of the new center will be partly offset by a special city tax on Washington hotels and businesses that would benefit from any large influx of convention-goers.

An aide to Leahy said yesterday that the restrictive language is designed to prevent convention center officials from seeking major concerts and sporting events instead of booking conventions that generate more tax revenue.

"If the schedule of conventions is cut back, then the revenues to the city will be significantly reduced and the whole rationale of the convention center . . . will be undermined," the aide said.

The convention center dispute has delayed enactment of the city's appropriations bill for the fiscal year that began Oct. 1. The D.C. government has been operating under a stop-gap spending bill approved by Congress. Most city agencies have been spending at fiscal 1982 levels, according to Budget Director Gladys W. Mack.