The long-simmering rivalry between Nancy Reagan and Raisa Gorbachev flared up anew Wednesday, with the American first lady acknowleging they were in a "Mexican standoff."

Although the two women maintained an appearance of cordiality and near-constant smiles during a brief tour of an icon storage vault, their last one-on-one get-together of the Moscow summit erased earlier attempts to paper over the strained impasse that marks their relationship."I want to say something. I want to say something now, OK?" Mrs. Reagan cut in at one point as Mrs. Gorbachev attempted to stop the press from questioning the American first lady.

Mrs. Gorbachev backed away, but pointedly looked at her watch as the U.S. first lady chatted a bit with members of the White House press corps.

The incident recalled a similar one during the December summit in Washington, when Mrs. Gorbachev lectured frequently on U.S. history, art, and political life, leaving Mrs. Reagan attempting to get in a few words.

Elaine Crispen, Mrs. Reagan's press secretary, said after the event, "They are from two totally different worlds."

Noting that Mrs. Reagan has spoken out more in Moscow than she did at the Washington summit, Crispen said she believed the two wom-en now had "more balance" and equality in their relationship.

Instead of meeting Mrs. Reagan as planned by the door of the vault, Mrs. Gorbachev had entered first and informed the waiting press corp that they could have "a dialogue" about the art. "The guests are late," she noted.

After Mrs. Reagan arrived and the two women shook hands, Mrs. Gorbachev presented the first lady with a bouquet of roses and a large coffee-table style book of pictures from the gallery.

She also presented reporters with a copy of the same book, proposing that they give it to "whoever has covered the summit best."

Mrs. Reagan raised her eyebrows in a look of mild consternation. She then stepped forward, and insisted that she be given equal time with the journalists.

She thanked Mrs. Gorbachev and the gallery staff for making arrangements to allow her to see the now-closed museum works, and said she was aware that very few people were granted a chance to view them.

When reporters tried to question the two women, Mrs. Gorbachev responded, "We have decided there would not be any interviews. Please allow us to show Mrs. Reagan the remaining art."

She retreated to the background, however, when journalists continued pressing for time with Mrs. Reagan.

Told that Mrs. Gorbachev had spoken at length about the icon collection, but had not mentioned it's religious heritage, Mrs. Reagan responded, "I don't know how you can neglect the religious implications. I mean they are there, when you see them."

The first lady said she was pleased with her visit and that she hoped to return so that she might be able to view the artistic and architectural treasures of the nation once again.

Asked if she'd become a convert to communism during her trip, the first lady laughed heartily, saying, "Oh, no." And she said Soviets weren't ready either to convert to capitalism.

Mrs. Reagan indicated that the five-day trip, her first to the Soviet Union, had not changed her views. "We have two different ways of living, two different philosphies," she said.

Asked about her relationship with Mrs. Gorbachev, the first lady laughed at the maneuvering that had just occurred, shrugged, and declared, "a Mexican standoff."

Mrs. Reagan had requested a viewing of the famed icons of the Tretyakov Gallery. Since the museum has been closed for renovation, the first lady was allowed to view a collection of the art in a high-tech, temperature controlled storage vault.

Even though the two women had tried to paper over the reports of a feud, Mrs. Reagan left the impression during a day trip Tuesday to Leningrad that she'd just as soon let the subject drop.

In a meeting with reporters aboard her plane, Mrs. Reagan said the Soviet people "are very warm and very open" but that she was less impressed with her high-level contacts. "Their philosophies and positions are completely different from ours," she said.

But given the repeated hand-holding between the first ladies during a tour of Kremlin churches on Sunday and at later official functions, Mrs. Reagan was asked who started it all.

"I don't know. It just sort of happened," the first lady said with a shrug of her shoulders.