MIAMI, SEPT. 10 -- President Reagan, meeting privately with Pope John Paul II, promised today that the United States is committed to a negotiated peace in Nicaragua and tried to enlist the pontiff in an effort to persuade the Sandinista government to make genuine democratic reforms, administration officials said.

Reagan said he told the pope that the United States is "unshakably committed to establishment of an enduring world peace and to the extension or expansion of human freedom around the globe," adding that "without freedom, there can be no peace."

The pope, in a 12-minute reply to Reagan's four-minute statement about the meeting, emphasized past and present U.S. contributions to individual freedom but called upon the United States to share its wealth with poorer nations. "The more powerful a nation is, the greater is its responsibility," the pope said.

Reagan emphasized political issues in his statement to the pope and reporters after the meeting. "I assured His Holiness that the United States is committed to the extension of democracy throughout Latin America," Reagan said.

He said he also told the pontiff that the United States and the Soviet Union are near agreement on a pact to remove medium-range nuclear missiles from the superpower arsenals but that achievement of the pact "depends upon Soviet willingness to get down to the hard work of completing an agreement."

A senior official said Reagan's appeal to the pope for pressure on the Sandinistas, which came on the day that the administration announced a new $270 million aid request for rebels seeking to overthrow them, was "conveyed in discreet diplomatic language."

The official said the president made no direct request for papal intervention in the Central American peace process but stressed the importance of Nicaraguan Cardinal Miguel Obando y Bravo's role. Fitzwater said before the meeting that "the president will welcome" the cardinal's "participation and urge the pope to take an active interest in his work."

Obando, an outspoken critic of the Sandinistas, heads the National Commission on Reconciliation, which is supposed to analyze and report on Sandinista efforts to restore democracy.

White House officials have said privately that the government named him to the position in part because he plans to be out of the country during much of October attending to church responsibilities.

Officials said Reagan, in stressing the importance of the cardinal's role in the peace process, hoped that the pope would free Obando of some of his church duties and encourage him to remain in Nicaragua during this critical period.

At the start of Reagan's meeting with the pope, reporters asked Reagan why he is pushing for aid to the contras while advocating peace in Nicaragua.

He initially declined to answer the question but, when asked again as he posed for a photograph with the pontiff, Reagan said, "Just because an agreement has been signed that will call for some waiting, you can't let them {the contras} starve."

The president referred obliquely to his Nicaraguan policy and U.S. support of rebels in Afghanistan in greeting the pontiff at Miami International Airport.

"In Latin America and Asia, we are supporting the expansion of human freedom, in particular, the powerful movement toward democracy," Reagan said.

White House spokesman Marlin Fitzwater said Reagan values the pope's counsel on Nicaragua because John Paul II has visited there and because "the church has been heavily involved in Central American affairs."

On Air Force One en route to Miami, Fitzwater had announced that Reagan will meet next Tuesday for "substantive" talks on arms issues with visiting Soviet Foreign Minister Eduard Shevardnadze.

Before today's meeting with the pope, White House officials were told that the pontiff wanted to discuss world peace, arms control and the prospective U.S.-Soviet summit in late November.

But Fitzwater said the Soviets have not told U.S. officials whether Soviet leader Mikhail Gorbachev is agreeable to a summit then. He said the administration does not know if Shevardnadze will bring a message to Reagan from Gorbachev next week.

However, U.S. officials are behaving as if the treaty and the prospective summit remain on track. Fitzwater said the Reagan-Shevardnadze meeting would be held at midday and last at least a half-hour, perhaps an hour.

"It will be an opportunity for them to discuss the progress of the arms talks," he said.

Shevardnadze and Secretary of State George P. Shultz then will hold three days of talks, and Fitzwater said the two will meet again the following week in New York, where Reagan is to address the U.N. General Assembly Sept. 21.