A slightly nervous Nancy Reagan and some slightly curious Washington reporters had their first official encounter yesterday. It lasted 12 minutes.

She turned aside the only question anyone attempted to ask with a mild rebuke that the gathering was "not a press conference."

The White House, in a media advisory issued last week, called the session "a background briefing" whose purpose was to allow Reagan to introduce her staff and to provide information on the Foster Grandparent Program, a project involving elderly volunteers administered by the federal agency ACTION.

It was when the first lady wound up her presentation on foster grandparents, a program she became interested in in 1967 when her husband was governor of California, that veteran White House correspondent Helen Thomas spoke up.

"You're not going to let your husband cut it out, are you?" Thomas asked, referring to the president's proposed cuts in the federal budget, many of which are expected to affect agencies such as ACTION.

"It's not a press conference, Helen," the first lady said, standing behind a lectern in the White House theater and slipping her foot in and out of a burgundy-colored pump. "But no, I'm not. Nor would he want to."

She left the theater advising reporters than they had better "get your Kleenex" out for the film they were about to see on the program in which 17,370 foster grandparents care for 43,425 retarded, disturbed and handicapped children in 50 states. Staying behind to answer questions for her were ACTION officials.

Reagan, wearing a pink-and-rose suit, opened the session by noting that "I understand you all have been wondering what I'm doing. As I said in my book ["Nancy"] and in lots of interviews, I'm a nester by nature. Until I can get all the boxes undone and unpacked and things put away I'm not much good to anybody."

Anxious to make the White House "homey," she said she had been spending all of her time unpacking the personal things and clothing the Reagans brought with them from California. But she also had been assembling her East Wing staff "in between packing cases" and she understood that it was a practice of first ladies to introduce their staffs to the press.

The East Wing's "token male," she laughed, insisting that he stand up, was Peter McCoy, her staff director. Then she introduced four other senior staffers: social secretary Mabel "Muffie" Brandon, press secretary Sheila Patton, assistant press secretary Barbara Cook and projects director Ann Wrobleski.

Earlier in the day, Reagan said she met with officials from ACTION and was surprised to learn that only 208 programs exist around the country.

She said she would like to involve "the private sector." She plans to attend a June meeting of program directors here and will tape broadcast "spots" for use during May, which is designated Older Americans Month.

McCoy said it seemed "peculiar" to him that a first lady would hold a press conference. Compared to what she had to do on the campaign, he said, yesterday's session with some 75 reporters had been "a piece of cake."