The Secret Service has quietly resolved most of its concerns about the security threat posed by the new Metropolitan Square office complex, the 12-story building whose rooftop offers a nearly unobstructed view of the North Portico of the White House.

Secret Service officials and representatives of developer Oliver T. Carr said yesterday they have had a series of "productive" meetings dealing with security at the newly completed 148-foot office building at 15th and G streets NW.

Those meetings also focused on safety problems arising from the planned adjacent 157-foot-high second phase of the project, which includes the controversial plan to demolish the historic Rhodes Tavern, located at 15th and F streets NW.

The Secret Service would not discuss specific details of their security plan, but government officials familiar with the issue said yesterday it includes stationing agents on the building rooftops during special White House events and overseeing the Carr company's security system.

The White House security issue surfaced two months ago with the disclosure that D.C. government officials, who approved height increases for the two-phase project, were never informed that the Secret Service considered the height of Carr's project a potentially "serious" security threat.

"Through our discussions with the Carr people, we are convinced we will be able to resolve our concerns," said Jack Smith, the Secret Service deputy assistant director for public affairs. "It has not been totally resolved as yet. But we are hopeful that it will be."

Michael McGowan, Carr's director of development, said staff members met several times with the Secret Service and "we are under the impression that there are no significant problems, no unsolvable problems to our operation" of both phases of the project.

According to officials familiar with Metropolitan Square, the second phase poses a potentially more serious concern than the first because the nine feet of additional height includes an elevator with direct access to the rooftop terrace. The added height needed for the rooftop elevator was approved by the Board of Zoning Adjustment May 4.

To assure security, McGowan said, "We have security personnel in our buildings at all times, whenever they are open. And we will continue to do that at Metropolitan Square." McGowan said additional security measures are contemplated, but would not discuss them.

Sens. Charles McC. Mathias (R-Md.) and Thomas Eagleton (D-Mo.) have requested explanations from city officials and from the National Capital Planning Commission (NCPC) to determine why the Secret Service's opposition to the project in 1979 was not made known to officials who were considering Carr's request to raise the city height limit from 95 feet for his project.. Various city and NCPC officials said recently they assumed that other agencies were following up the issue.

Mathias, who heads a Senate subcommittee that oversees District affairs, has also asked the involved parties for an explanation of security measures taken.

Smith said the Secret Service plans to meet shortly with Mayor Marion Barry, NCPC members and other officials to discuss the security plans.

Supporters of the preservation of the 183-year-old Rhodes Tavern had hoped that the Secret Service concerns about Metropolitan Square security would somehow delay the second phase construction project, which calls for demolition of the tavern that was Washington's first town hall.

McGowan said the developer hopes to begin demolition within a few months, and begin construction later this year.

D.C. voters will be asked in November to approve a nonbinding initiative calling for preservation of Rhodes Tavern, but the chief architect of that initiative said yesterday that with the Secret Service's concerns resolved, the Carr firm may proceed quickly with demolition--possibly before November. Joseph Grano, president of the Citizens Committee to Save Historic Rhodes Tavern, said the city has begun processing Carr's application for a construction permit on the tavern site.

Grano has asked Barry to deny Carr's permits until after the November initiative, but Barry has taken no stand on the question, Grano said.