Italian Prime Minister Giovanni Spadolini hosted a sparkling party at the Italian Embassy last night in honor of the Vice President and Barbara Bush, against a backdrop of Italian concerns about East-West trade relations.

Earlier yesterday, Spadolini met with President Reagan to discuss the recent U.S. decision to extend an embargo on equipment for the Siberian gas pipeline to European companies operating with American licenses. The embargo threatens a multimillion-dollar Italian contract to supply the Soviet Union with costly machinery for the pipeline.

"The prime minister is optimistic that the problem will be solved," said Italian Ambassador Rinaldo Petrignani during cocktails.

"I'm not going to speculate at this point on a solution," said presidential counselor Edwin Meese. "The prime minister is looking foward to an agreement . . . we are looking foward to working with him towards an acceptable solution."

In his lengthy toast to Bush, Spadolini steered clear of the trade rift, but stressed "the need for the coordination of our policies . . . and the need to make every effort to reach joint decisions on matters of common interest and with a view to common goals."

International concerns aside, it was domestic chatter that most fascinated the 60, mostly Republican, guests between bites of warm almonds and smoked salmon. That is: The Election. They didn't seem to mind it.

"You have come here at an interesting time for us," Bush told the prime minister. "We're quite pleased with our new senator from California Pete Wilson . It was a very important state for us."

A few minutes later, Bush minimized Democratic gains nationwide, and in the House.

"Well, I'd rather we had picked up 26 seats in the House, but this is an off-election year and people will analyze it as an off-election year," Bush said. "There was some good, some bad, but we came out all right. I think the country was saying it is not looking for a major shift."

"I'm not discouraged," said Agriculture Secretary John R. Block. "It's a good sign that we didn't lose any seats in the Senate. It was quite an expected result for an off-year . . ."

"I don't think the election changed all that much," said Commerce Secretary Malcolm Baldrige. "If there was a message in it, the people do not want a change, otherwise the shift would have been greater."

"Everyone I talked to was tickled to death with the results," said Protocol Chief Selwa Roosevelt.

The formal evening began about 8 in the soft oyster-and-peach drawing room at the grand embassy, the former Guggenheim estate. An impressive array of Washington politicos gossiped shop talk and devoured the almonds. "I keep popping them," lamented Bush. Everyone hugged hello, European-style.

Among those popping and hugging were: Secretary of State George Shultz; Deputy Defense Secretary Frank Carlucci and wife, Marcia; National security adviser William P. Clark and wife, Joan; Undersecretary of State Lawrence Eagleburger and wife, Marlene; Joseph Califano, former secretary of Health, Education and Welfare, and Sen. Patrick Leahy (D-Vt.).

Guests filed into the dining room for a dinner of bluefish, fillet in Barolo wine, artichokes au gratin and a spectacular fruit and sherbet dessert. Security for the evening was particularly tight, with hordes of American and Italian press scurrying around.

Even Anne Petrignani, the Italian ambassador's wife, thought so.

"I went grocery shopping today and they wouldn't even let me back into my own house," she said. "They said, 'What do you want?' I told them I lived here . . . And they finally believed me."