President Luis Alberto Monge of Costa Rica said yesterday he has asked for security-related assistance from the United States and other countries in the face of growing terrorism and military incursions along the border with Nicaragua.

Monge said President Reagan and Secretary of State Alexander M. Haig Jr. appear to be giving serious study to providing uniforms and communications equipment for enhanced police and anti-terrorism forces, following the Costa Rican's request to Reagan in a White House meeting Tuesday.

The Central American state has long been known for its unarmed democracy. Last August, Monge's predecessor, Rodrigo Carazo, indignantly denounced U.S. Ambassador to the United Nations Jeane J. Kirkpatrick for suggesting the possibility of American military aid for his country. At the time, Carazo declared that Costa Rica was "pacifist in word and deed" and determined to remain so.

Monge, in an interview with Washington Post editors yesterday, said no consideration is being given to creation of a regular army. But he said that Israel and Venezuela, in addition to the United States, have been asked to supply help to Costa Rican security forces.

Israeli Prime Minister Menachem Begin, who met Monge here Monday, "gave every indication he is very willing to help," Monge said. The Costa Rican also said his country's police forces have been sent to Venezuela for training.

State Department officials said the request for security-related assistance is under consideration. Since the request had not been anticipated, officials said, it will not be easy to find the funds in current budget allocations.

Preliminary exploration of supplying less than $10 million in U.S. military aid is reported taking place in the administration. An official pointed out that U.S. aid to police abroad is prohibited by law.

Costa Rican Foreign Minister Fernando Volio, relating the increasingly serious security problems to his country's economic woes, said it would cost $1 million per year just to send a unit of the existing rural guard to the Nicaraguan border to deal with the "constant harassment" by better trained and equipped Sandinista military forces.

The economy of Costa Rica, which owes $2.6 billion in foreign debts and is unable to pay, "is in a shambles," according to an Agency for International Development (AID) document supplied to Congress in recent weeks.

The country is in the midst of negotiations with the International Monetary Fund for a stabilization plan involving major new austerity measures. Monge expressed optimism yesterday that agreement will be reached.

Costa Rica's main hope for early U.S. aid lies with the administration's Caribbean Basin Initiative, which is in trouble in Congress. Monge spent much of his time here this week lobbying for passage of that plan, which includes $70 million for his country.

In a related matter, an administration official renewed the official plea yesterday for $5.1 million in aid to "private-sector activities" in Nicaragua. Assistant AID administrator Otto Reich said the funds, a continuation of an existing program, would provide "political and moral support" to Nicaragua's Roman Catholic Church and other elements of the private sector opposed to the Sandinista regime.

Failure to provide the money, according to testimony by Reich to the House international operations subcommittee, could be interpreted in Central America to mean: "Don't count on the United States for help when the situation gets difficult."