The National Capital Planning Commission yesterday gave unanimous final approval for construction of the controversial $6 million Vietnam Veterans Memorial here.

Construction is expected to begin near the Lincoln Memorial in about two weeks.

All that remains before construction can begin is for Interior Secretary James G. Watt to give his approval to the project.

Watt personally intervened in January when some veterans and congressmen launched a last-minute campaign for a "traditional" war memorial. Two dozen Republican congressmen, in a letter to President Reagan, attacked the V-shaped, black granite wall memorial for making "a political statement of shame and dishonor."

Watt announced last month he would hold up the project until he saw final design plans and was assured there was sufficient money to build the memorial. The fund has now raised close to $6 million. Memorial supporters believe Watt's concerns have been met and expect his approval of the project today.

The wall memorial, chosen last May after a national design competition, is to be cut into a small hillside in Constitution Gardens. It will contain the names of the 57,692 American war dead.

In a concession to critics of the design, the nonprofit Vietnam Veterans Memorial Fund two weeks ago agreed to support construction of a flag pole and a larger-than-lifesize statue of a soldier to go beside the wall.

The statue and flag pole, however, will have to be approved by NCPC, the Fine Arts Commission and the Joint Committee on Landmarks, approval which may be difficult to get. The federal agencies endorsed the simple wall design in part because it would not detract from the Lincoln Memorial, only 600 feet away.

The memorial is expected to be completed in time for dedication on Veterans Day, Nov. 11