Prince George's County Executive Parris Glendening and D.C. Mayor Marion Barry strode purposefully into a county conference room yesterday to face about a dozen reporters and camera operators, in the first official visit between the leaders of the Washington area's most populous jurisdictions.

The two had just spent an hour discussing common themes, including Metro construction and costs, sludge treatment, and ways in which the county could support the District's efforts to attract the Democratic National Convention in 1984.

The talk yielded "few details," said Glendening, but showed a willingness to work together. At one point they pinned to their lapels red, white and blue buttons that read, "Washington '84, it's logical."

"This was serious business we're talking here," said Barry, when asked if the session had been largely a social call, "The District is spending $92 million out of our budget on Metro alone. I wouldn't call that chit-chat."

According to an aide who attended the earlier meeting, the two agreed chiefly to try to expedite the construction of Metro's Green/Yellow line to Greenbelt, which is currently stalled by the District's inability to select an alignment that would connect the Fort Totten station with Prince George's Plaza.

Glendening asked how he could help Barry's drive to lure the Democratic National Convention and agreed to participate in a February presentation and to await further instructions. They then agreed to keep each other informed on future uses of a vacant, District-owned hospital in Seabrook. They concluded by discussing their common desire to contain Metro operating costs.

The idea for the meeting came soon after the November elections, both men said, when Glendening was elected to his first term and Barry to his second, both by comfortable margins. Barry called his fellow Democrat to offer his congratulations and to suggest the meeting.

Barry traveled the 25 miles from downtown Washington to the county seat of Upper Marlboro in style yesterday, speeding along Pennsylvania Avenue in a dark blue sedan with a blaring siren, just shy of the 10 a.m. meeting time. A group of construction workers toiling at an intersection along the way jumped up and cheered his car as it maneuvered its way onto the left shoulder and passed a group of four cars stopped at a red light.