Washington — Patting the trunk of an elephant, holding a televised press conference, or dedicating a new office building of the National Geographic Society, President Reagan seems to be exuding self-confidence these days.
As the Democrats struggle to put their house in order, the President is seen by political observers as very much ''on top,'' carrying out his duties against the backdrop of several successful trips abroad, a continuing lead over Democratic contender Walter Mondale in the political polls, and a robust economic recovery.
White House aides say they see no difference in the President -- that he has consistently exhibited a sense of security in his job and in himself. But outside observers detect a heightened self-assurance.
''He's now optimistic not only about the country but about his own leadership of the country,'' says Stephen Wayne, a presidential scholar at George Washington University.
''Reagan is at the peak of his form,'' says a European diplomat. ''The trip to Europe went off extremely well from his standpoint. He maneuvered through the political minefields in Ireland, delivered a talk on D-Day made for him, and avoided a confrontational summit in London.''
Mr. Reagan's press conference last week reflected this success. Political analysts agree that he handled it masterfully, deftly fielding questions on the sensitive issue of a summit meeting with the Soviets. Although he made some factual errors about the economy, the President was fully in command -- even throwing off humorous one-liners.
''He was always a President that could communicate at home,'' says Professor Wayne. ''But he now seems in his own mind to feel himself a world leader.''
Not unlike other presidents, Reagan has gradually turned his attention and interest to international affairs, even while difficulties with Congress have grown. In the process he has learned, and now seems more comfortable at home and abroad.
''He looks like a man who enjoys his job, and we have not had a man in that posture for a long time,'' says Thomas Mann, executive director of the American Political Science Association.
Political and diplomatic experts are struck by the extent to which Reagan has modified his foreign policies as the November election approaches. He has adopted a conciliatory tone toward the Soviet Union, for instance. He has softened his position on antisatellite weapons. He is putting a little less emphasis on military confrontation in Central America. And he is conspicuously refraining from intervention in the Persian Gulf without being asked first by the Gulf states.
''He's trying to moderate his rhetoric because of the genuine problems that exist for him,'' Dr. Mann says.
''All or much of this is related to the judgment of people around him and of the Republican senators about what is necessary for the campaign,'' says David Newsom, director of the Institute for the Study of Diplomacy at Georgetown University. ''I'm not sure how fundamental the change is.
''But Reagan is a fire horse now who is feeling the excitement of the campaign. . . .''
Democratic analysts don't deny that the President conveys a strength of leadership that will make him difficult to defeat in November. But they also see factors that could favor the Democrats:
* Many people participated in the recent Democratic primaries who normally do not vote much. A New York Times survey, based on exit polls, found that blacks, women, union members, and members of the ''baby boom'' generation constituted a larger share of primary voters than usual. Voters from union households, for instance, represent 30 percent of all Democrats but cast 33 percent of the votes.
* Reagan's present nine-point lead over Walter Mondale in the Gallup poll is not deemed that large, given the high visibility the President has had with his trips overseas. Moreover, if the Democrats field a Mondale-Hart ticket, even that Reagan lead narrows to only four points.
* After the convention the Democrats can be expected to be much more united, ready to put the issues on the table and to go out after independent voters. An incumbent always looks presidential when the other party is squabbling.
''The Democratic vote is going up among blacks, unions members, and others,'' says Ann Lewis, political director of the Democratic National Committee. ''So the level of Reagan's popularity is shallow, and coming up is a rising tide of election activity. Some 30 to 40 percent of the people say they won't vote for Reagan, and for someone who's been in office four years, that's a high number.''
Republican planners do not conceal their confidence in the President. ''He exudes a strength of leadership that comes through very easily to the public,'' says William Greener, communications director of the Republican National Committee. ''People are noticing that his attitude and approach are a contrast to what was there four years ago. Reagan . . . is not overwhelmed. He's in control.''
But both White House and GOP campaign officials are operating on the expectation that the race could be close. ''In almost every campaign cycle, the month of September finds things closing up,'' Mr. Greener says. ''It is inevitable that a tightening occurs. We're confident that we're on a winning team. But you never know when a foreign-policy or other potential obstacle arises.''
Among the GOP concerns is a continuing rise in interest rates or a foreign policy development that could involve US troops. But Reagan political planners are also aware that it is sometimes a minor, unexpected occurrence -- a mistake in a debate, for instance -- that can cause problems for a candidate. The word has therefore gone out not to let up in organizational planning.