There's nothing like talk of a U.S. arms deal to put a foreign country in the headlines -- and its embassy in fashion and on the party circuit in Washington. Take Pakistan.

On Saturday in Lslamabad, Pakistan's foreign minister, Agha Shahi, expressed interest in buying American arms at a discount. Yesterday at the Pakistani Embassy here, several hundred people crowded in for lunch.

"I think it's in," said one World Bank official of the martial-law country that may get increased aid from the Reagan administration. "But how long it'll stay in, I don't know."

The official reason for the lunch was National Day. Just as American embassies overseas celebrate July 4th, almost every foreign embassy in Washington holds an annual reception in honor of its country's birth. These events serve several purposes. Among them: good will, essential hobnobbing with State Department officials and, in yesterday's case, a chance to eat extremely well.

Which may have been the other reason the place was packed.

"Marvelous lunch," said a second World Bank official as he ate barbecued chicken, spinach, rice, kooftah curry . . .

Dotted throughout the formal rooms of gilded columns and military personnel, you could find assorted State Department officials dining with equal enthusiasm. They were invited because of their expertise on Pakistan and their involvement in the current review of U.S. arms policy toward that country. They were also behaving like good State Department officials: They were keeping their mouths shut.

"We consider Pakistan a very important country in a region vital to our interests," said Jane Coon, deputy assistant secretary of state for South Asian affairs. "The policies are under review, but this is the moment not to go into specifics."

American diplomats here and in Pakistan also have been silent on the Reagan administration's proposals, believing they lost the chance to improve relations last year when plans appeared in newspapers before they reached the Pakistani government.

And at yesterday's lunch, there was another reminder to keep quiet: the presence of Richard Pipes, the National Security Council official who said last week that war with Russia was inevitiable if the Soviets continued on their present course. The White House muzzled him the next day.

Predictably, Pipes was enjoying a certain celebrity status at yesterday's lunch. "If you see him," one State Department official said to a Pakistani economist, "point him out to me. I want to see the man of the hour."

The man of the hour stayed only a half-hour, then left.

There was no Pakistani ambassador to give the party, since the last one has retired and a new one hasn't been appointed yet. So Majmuddin Shaikh, the embassy's charge d'affaires, was host. "This is the one step that we think would be logical," he said of his country's interest in buying U.S. arms. "In Washington now, there is a much greater realization of Pakistani problems and Pakistani importance."