At least 12 transatlantic flights were rerouted and some were slightly delayed yesterday as Portuguese air controllers continued a 48-hour boycott of U.S. flights in support of their striking American counterparts, the Federal Aviation Administration said. No flights were reported canceled, however.

Planes that usually fly nonstop between the United States and Portugal suffered the worst delays on Sunday, as they flew to airports in Canada, landed and took off again with new flight plans, airline spokesmen said. Because of those diversions, the Portuguese accepted the aircraft, as they were not coming directly from U.S.-controlled airspace.

But yesterday, at least one airliner coming in from Portugal filed a flight plan for Canada, then changed it in midair, a bureaucratic dodge that satisfied the Portuguese and cut delays. The flight, operated by TAP, the Portuguese national carrier, took off from Lisbon and was cleared to Montreal. But once in Canadian-controlled airspace, it proceeded directly to New York, arriving close to schedule yesterday afternoon.

Transatlantic flights that do not land in Portugal but usually cross Atlantic airspace that it controls from the Azores were diverted to two routes that the FAA mapped out along the 46th and 47th parallels, skirting north of the Portuguese zone.

Flying time is about 30 to 45 minutes longer on these routes than on the more direct Portuguese routes, an FAA flight specialist estimated.

FAA officials reported that the boycott was handled with only minor disruption overall. The Portuguese guide only a small fraction of transatlantic traffic, generally those flights headed for the Iberian peninsula, the Mediterranean countries, Africa and the Middle East.

In contrast, the Canadians control the "Great Circle," the main route to Western Europe, and were able to cripple transatlantic aviation with a similar boycott last week.

The Portuguese began their action at 8 p.m. Sunday. Earlier, they had scheduled a boycott, and then canceled it in response to a request from the International Federation of Air Traffic Controllers Associations. Later, the Portuguese controllers changed their minds again and rescheduled the boycott.

The federation plans an emergency meeting in Amsterdam Saturday to discuss a worldwide response to the U.S. situation if it remains unresolved. Last week, the federation's president called on President Reagan to resume talks with the American controllers, who left their jobs 15 days ago.

The administration has refused to have further dealings with the Professional Air Traffic Controllers Organization (PATCO), the U.S. union. After imposing a deadline to return to work or be fired, the government began dismissal proceedings against more than 11,000 strikers and is seeking to decertify the union.

Canadian controllers have charged that U.S. airspace -- now directed by teams of supervisors, military controllers and nonstriking civilians -- is unsafe and last week refused to route planes to or from it. Their boycott was a protest against poor safety levels, not a sympathy strike, union officials said.

But the Portuguese union has publicly expressed anger over the administration's hard line toward PATCO. A communique from the Association of Portuguese Air Controllers, quoted by Reuter, attributed its boycott at least in part to "the repressive way in which the U.S. government dealt with an industrial conflict, through condemnations, prison sentences and disciplinary measures, with total disregard to human rights and democratic coexistence . . . . "

Meanwhile, the FAA reported that major airlines continued to operate about 75 percent of their customary flights in and out of 22 major airports affected by "flow control" measures the FAA instituted after the controllers' strike began.