NEW YORK, SEPT. 28 -- Secretary of State George P. Shultz today stressed to foreign ministers of the Western Hemisphere the Reagan administration's concern that the five-nation Central American peace process will fail unless Nicaragua's Marxist government negotiates with the U.S.-backed contra rebels.

U.S. officials said that in a day-long series of meetings with Latin American and Caribbean foreign ministers, Shultz emphasized the U.S. position that under the peace plan, no party to it can declare a cease-fire unilaterally but must negotiate mutually acceptable arrangements with its opponents.

The ministers are here for the opening of the annual U.N. General Assembly meeting. Shultz met separately with nine of them, including two Central Americans: Rodrigo Madrigal Nieto of Costa Rica and Ricardo Acevedo Peralta of El Salvador. Tonight he was host to all of the Latin American delegations at a dinner on board a yacht that cruised around Manhattan island.

Among the guests who accepted invitations to the cruise were Nicaraguan Deputy Foreign Minister Victor Hugo Tinoco and Aristedes Sanchez, a member of the contras' political directorate.

In remarks for delivery during the cruise, Shultz said, "All of us are united in principle behind this solution; all of us realize that it will work only if we live by it in practice . . . . In Nicaragua, dialogue must move beyond rhetoric and abstract principle: we are still waiting to learn whether the government will agree to meet with all groups of the opposition, including the resistance, to negotiate their differences."

The Central American initiative, proposed by Costa Rican President Oscar Arias and agreed to by the five nations at an Aug. 7 meeting in Guatemala, set a Nov. 7 deadline for cease-fires in all regional conflicts. Particularly at issue are the conflicts between governmental and insurgent forces in El Salvador and Nicaragua. The plan does not specify that the governments must negotiate with their armed opposition.

Last week, Nicaragua's Sandinista government, which has refused to deal directly with the contras, said it would institute a series of partial cease-fires in areas where the contras operate. The United States subsequently denounced the Nicaraguan move as "a propaganda ploy" designed to make it appear that Nicaragua is complying while continuing to freeze the contras out of the peace negotiations.

The Sandinistas have indicated that they might be willing to let Cardinal Miguel Obando y Bravo, head of Nicaragua's reconciliation commission, act as intermediary with the contras. So far, though, there has been no formal movement on that idea, and there are questions about whether Obando, who is scheduled to be at a papal synod in Rome throughout October, will be able to undertake such a mission.

The United States has said it welcomes the peace initiative. However, President Reagan's continued criticism of Nicaragua and his insistence that he will never desert the contras have caused widespread speculation in Latin America and the U.S. Congress that he wants to keep trying to overthrow the Sandinistas by force.

State Department spokesman Charles E. Redman repeated today that Reagan and Shultz want to help make the Arias plan work. To that end, he added, Morris D. Busby, the U.S. liaison to the peace talks, will return to the region Wednesday for further talks with the four democratic countries -- Costa Rica, El Salvador, Honduras and Guatemala -- taking part in the negotiations.

But, Redman insisted, real peace requires a role for the contras in working out a cease-fire and subsequent moves toward defining Nicaragua's future political life. He noted that El Salvador's President Jose Napoleon Duarte has set in motion a process, to begin Oct. 4, of discussing cease-fire arrangements with the leftist guerrillas fighting his government.

Redman also noted that Costa Rican President Arias had agreed during a meeting with Reagan at the White House last week that unilateral cease-fires did not meet the specifications of his peace plan.

"We agree with President Arias that a cease-fire is not something that can be negotiated unilaterally but rather is something that has to be discussed with those on the other side," Redman said.

Redman also announced that Shultz will visit Israel and other Middle East countries for four days before going to Moscow for talks Oct. 22-23 with Soviet Foreign Minister Eduard Shevardnardze.