The U.S. General Accounting Office raised strong new doubts yesterday whether the District could build its proposed new downtown convention center for the estimated cost of $110 million, largely because of its construction timetable is so tight it may not be attainable.

The GAO, in a report prepared for the Senate District Appropriations Subcommittee, also questioned whether the center would attract as many visitors to the city as are anticipated, and whether the District government could "provide for the effective management seen as critical to (the center's) success."

In releasing the report, Sen. Patrick J. Leahy (D-Vt.), the subcommittee chairman, said he would "have a series of hard questions for the city that must be answered" at hearings before a decision can be made on granting congressional approval for the project.

The report by GAO, an auditing and investigatory arm of Congress, did not make any recommendation on the project, but focused on its apparently most vulnerable aspects.

Ben W. Gilbert, the District's municipal planning director and a leading supporter of the project, challenged the GAO's findings in a letter released with the report. Although rigid, the timetable and the cost estimate can be met, he said.

The center would be built on a 10-acre site on the south side of Mt. Vernon Square, site of the old D.C. public library, and would be open for business in 1981.

The D.C. City Council has taken preliminary steps to acquire the land and design the project, but it needs approval from four congressional committees before it can borrow the money to proceed.

In its six-week look at the project, the GAO focused on these points and raised these questions:

Is it realistic to expect the center to draw between 310,000 and 390,000 more convention delegates to the city each year, considering a growing competition from other cities and from an enlarged Sheraton-Park Hotel? "Anticipated financial benefits (to the city) will be reduced to the extent that this estimate is overstated," the GAO found.

Can the timetable for construction be met? The report noted that - among other things - a time-consuming environmental impact statement must be prepared and reviewed. That could add up to 10 1/2 months to the construction timetable, with resulting cost escalation and an erosion of the financial projections. Also, there is a significant problem of relocating residents and businesses now on the site.

Can the District recruit "an efficient promoter, salesman and administrator" to manage the center? This is needed, the GAO said, and in any event, management should not be vested in any department of the city government.