Leaders of the D.C. statehood convention, paralyzed by bitter parliamentary bickering among delegates and rapidly running out of time, moved yesterday to ask the City Council for another four weeks to finish writing a proposed constitution in the city's bid for statehood.

The convention's beleaguered executive committee, headed by president Charles I. Cassell, asked the 45-member convention to authorize a formal request for emergency legislation that would extend the 90-day, $150,000 session from May 29 to the end of June--without pay for the delegates if necessary. The convention will vote on the extension next Saturday.

The City Council and Mayor Marion Barry have shown little interest in the past in granting more time or money for the convention. But convention delegate James A. Coates said council chairman Arrington Dixon's office recently indicated willingness to seek "some kind of extension" without specifying the time or money. Dixon could not be reached for comment yesterday.

Meanwhile, the mood on the ninth floor of the old Pepco building at 10th and E streets NW, where the convention is taking place, is one of urgency and gloom.

With 28 days to go, only a fraction of the proposed constitution--a preamble and a 20-page article on the judiciary--has been completed on a preliminary basis. Hundreds of pages remain to be debated and approved. Protracted fights on the bill of rights, local government and other elements are expected.

Since its beginning March 1, the convention has been plagued periodically by internal bickering, stalling tactics, shouting matches, sparse attendance, staff shortages and frequent breakdowns of the office machines used for duplicating documents. City funding is starting to run out.

"I don't know if we're going to make it," said Ward 5 delegate Harry Thomas Friday night, his face drawn with fatigue.

"We're in the kind of panic a legislature usually has on the last day--but we're in the last month," said Coates yesterday.

Nerves are frayed. Delegates, most of them working regular nine-to-five jobs during the day, have been meeting five and six nights a week. Cassell became ill last Thursday night, leaving the convention exhausted. A week earlier, convention first vice president James Baldwin was hospitalized with chest pains. His doctor told him to slow his convention activities to three nights a week.

Two delegates--Thomas and Courts Oulahan--resigned in disgust from the convention's judiciary committee last week after the convention narrowly rejected their proposal for appointed judges and adopted instead a system in which judges would face periodic "retention elections" by city voters. (Thomas later rejoined the committee.)

Delegates interrupt and snap at each other. "Why don't you shut up, man. Who the hell you think you are?" snarled Ward 1 delegate Maurice Jackson at convention secretary William Cooper last Wednesday.

"Sit down; you are out of order," yelled Cassell at Ward 3 delegate Gloria Corn as she repeatedly interrupted other speakers debating the city's proposed new court system last week.

In addition to the raucousness, several delegates have engaged in prolonged arguments and stalling tactics to push through amendments considered unrealistic, too experimental or too radical by the majority.

Ward 2 delegate Kenneth Rothshild, for example, proposed that two of the nine supreme court justices of the proposed judicial system be lay persons. Ward 2 delegate Brian P. Moore pushed for a network of "neighborhood courts" with nonlawyers as judges.

When other delegates protested the lengthiness of debate, Moore and Rothshild complained of efforts to stifle dissent and the free flow of ideas.

With the time crunch getting closer, Cassell, Baldwin and others last week attempted to impose tighter parliamentary discipline. Cassell appointed a five-member "committee on decorum."

Ward 4 delegate Jeannette Feely suggested that committee members should "tap delegates on the shoulder when they're out of order . . . and if that doesn't work, then maybe we need to call in the guards."