Nancy Reagan and Raisa Gorbachev toured Kremlin churches Sunday, holding hands and dismissing their reported feuds as "rumors," but when talk turned to religious activities, the Soviet first lady abruptly cut the conversation short.

While President Reagan and General Secretary Gorbachev squared off over human rights inside the Kremlin's Great Palace, the two women wore smiles and strolled hand-in-hand toward the cameras in an attempt to put to rest the stories about the tense relationship that emerged from their last meeting at the Washington summit."We've gotten along very well every other time," a smiling Mrs. Reagan said in response to queries about the supposed frosty relationship.

The Soviet first lady, true to the forthright style she displayed at the White House, chimed in at length and insisted that she considered such reports frivolous.

"Rumors have it, and there was a question, that there is some misunderstanding between myself and the (president's) wife," she replied through an interpreter. " . . . I would like to say, I think it's not serious."

Mrs. Gorbachev said her contacts with Mrs. Reagan have been part of the ongoing improvement in relations between the two superpowers. "We do have a lot to talk about and we are going to have something to remember, which is very important. I welcome Mrs. Reagan here and the president to Moscow," she said.

At one point, Mrs. Reagan was asked whether former White House chief of staff Donald T. Regan incorrectly portrayed her in his book as having asked, after an extended dinner lecture from Mrs. Gorbachev, "Who does that dame think she is?"

Mrs. Reagan, with an icy stare, replied curtly, "Yes."

Even though the two women offered nearly constant smiles, the first lady did display a bit of the impatience she'd shown during the Washington summit as Mrs. Gorbachev maintained an extensive dialogue with the press corps.

During a tour of the Kremlin's sun-splashed Cathedral Square and its ancient, golden-domed stone churches, the two first ladies were often shoulder-to-shoulder, pointing at the sights and talking through interpreters about the fortress' collection of buildings that served as the residence, places of worship and tombs of the Czars.

Mrs. Gorbachev, attired in a fitted, winter white wool suit and dark suede high heels, repeatedly patted the back of her neck to smooth her closely-cropped red hair. On her left shoulder, she wore a gold and green-stone firebird, a famous figure in Russian fairy tales. Mrs. Reagan wore a black-and-white checked Oscar de la Renta two-piece suit, complete with black patent heels and purse and white pique bowed blouse, all set off by a matching set of gold and black bracelets, sparkling earrings and a large stone ring.

The Soviet first lady quickly took charge of the tour as she put her arm about Mrs. Reagan's waist and guided her about the inside the 14th century Cathedral of the Annunciation, the largest and one of the oldest churches-turned muesums in the Kremlin.

The vaulted stone church, crowned with five gilded domes, has 40-foot high walls covered with a rich collection of priceless paintings and icons that show scenes from the life of Christ and the Virgin Mary. It is the repository of the finest and most revered icons in Russia, some dating from the 12th century, brought to the church and restored.

After they entered the Cathedral, Mrs. Gorbachev was asked about what she wanted to tell the American people about what the summit should produce.

"Peace and friendship and that they understand the Soviet people," she replied. Asked what else, the former university lecturer shot back, "What do you mean, what else? That's the most important thing."

Mrs. Reagan, appearing a bit bewildered, was asked her impressions of the Soviet Union. "Wonderful, very exciting, it's a little overwhelming," she replied, eyes wide and blinking.

At that point, Mrs. Gorbachev interrupted, insisting, "Please, I beg you, allow us to see the cathedral."

The Soviet first lady then guided Mrs. Reagan from reporters and launched into a lecture about the religious paintings that adorned the golden wall that divides the church sanctuary from its main hall. As they reached one icon depicting a sorrowful Virgin and the infant Jesus touching the mother's cheek, Mrs. Gorbachev remarked that it was one of the most beloved images in the nation.

"Very, very, very maternal," Mrs. Reagan remarked.

Mrs. Reagan then turned from Mrs. Gorbachev and towards the interpreter, asking, "Now let me finish," and she queried whether the cathedral was used mainly as a museum or for religious activities.

"Nyet," responded Mrs. Gorbachev, to which the first lady quickly replied, "Oh, yes, nyet, the word `nyet,' that I understand."

Mrs. Gorbachev then added that there had been no religious observances in the Cathedral since 1918, but the interpreter apparently corrected the date to 1917.

"It has obviously a very religious feeling," Mrs. Reagan said, softly of the paintings. She then turned to Mrs. Gorbachev and asked if it were true that a concert was planned for the cathedral during next month's celebration of the millenium, the observance of the 1,000-year anniversary of the spread of Christendom to Russia.

"Nyet," Mrs. Gorbachev replied curtly, putting her arm around Mrs. Reagan's waist, briskly guiding her out the door and jumping into a discussion of icons, frescoes, and wood carvings - out of reporters' earshot.

According to Mrs. Reagan's press secretary, Elaine Crispen, the two women held hands again as they took a walk along the Kremlin embankment that overlooks the Moscow River. Spectators applauded the two women as they strolled about the cobblestone square, and they then retired to the Great Kremlin Palace, where they had tea.

Mrs. Crispen said the two discussed the supposed feud, and she quoted Mrs. Gorbachev as saying, "All these rumors are trivial stories."

Mrs. Reagan then replied, speaking of the media, "Yes, but you can't get them to change their minds. I've told them so many times that the rumors are not true," Mrs. Crispen quoted her as saying.

The two ladies agreed that what was important was their husbands' work and the change in relations between their two nations, Mrs. Crispen said.