VENICE, JUNE 10 -- President Reagan's performance at the 13th economic summit left the other leaders of major industrial democracies convinced he has rather suddenly begun to show his age and lame duck status and wondering whether he possesses the energy and initiative to provide active leadership for the alliance, according to European diplomats.

This image of Reagan was reinforced in public today as the president appeared to be nodding off at the reading of the final economic communique. Treasury Secretary James A. Baker III and Secretary of State George P. Shultz seemed to nudge Reagan to keep him awake. Presidential spokesman Marlin Fitzwater said, "He stayed awake for the whole time, unlike some of his counterparts."

Reagan was also the only leader who spoke from prepared note cards in private meetings. Although Reagan frequently uses such cards, the technique seemed this time to add to the impression that his leadership role had diminished.

On complex issues such as the NATO doctrine of "flexible response" and the impact of eliminating medium-range missiles from Europe, British Prime Minister Margaret Thatcher and French President Francois Mitterrand took the lead at the opening dinner discussion.

The European diplomats said after the summit closed today that they were struck by the change in Reagan's demeanor from a year ago in Tokyo, when he was at the zenith of his popularity at home and played a leading role in discussions at the summit table.

His political standing at home tarnished by the Iran-contra scandal, Reagan came here hoping to invigorate his presidency by demonstrating his ability to guide and inspire other democracies.

Publicly, he was sanguine and upbeat, declaring today, "It's been a fine summit." But in private sessions, he was sharply challenged by the leaders of France, West Germany and Japan who criticized the enormous budget deficits of the Reagan years, despite Reagan's claim that he has made progress in reducing them.

Reagan's summit partners also expressed anxiety about the impact on allied defense strategy in Europe of a prospective agreement on limiting medium-range nuclear missiles. They also gave only lukewarm backing to Reagan's initiative for a greater naval presence in the Persian Gulf.

White House officials privately acknowledged the summit was not a high point for the troubled president. "That's just the way the summit goes," a senior Reagan assistant said.

White House officials strained to put a good face on the outcome and they announced Reagan would address the nation Monday on the summit from the Oval Office. They said the speech will also showcase NATO approval -- expected to be made final this weekend -- of the prospective medium-range missile treaty with the Soviets. As Reagan's first and only arms agreement, the emerging pact has become the one bright spot in his dealings with the allies.

European diplomats said, in contrast to the 1986 Tokyo summit, Reagan failed to make a strong case this year for a number of American positions and seemed preoccupied and distracted during the sessions. They noted that Shultz and Baker often carried the weight of speaking for the United States on important matters. In a meeting with Mitterrand today, Shultz intervened to remind the French leader that Reagan had pledged not to negotiate with the Soviets on France's and Britain's separate nuclear forces, a White House official said.

Reagan failed to meet even modest expectations raised for the Venice meeting. For example, prior to the summit, Reagan said he would propose that the seven industrial democracies set a goal of eliminating agricultural subsidies by the year 2000. But the final economic communique today did not include the proposal.

Treasury Secretary Baker said the idea was not raised in the plenary meetings because "there was not sufficient additional support for putting a fixed date in there."