A senior Nicaraguan leader today canceled plans to visit the United States on grounds that Washington was taking too long to decide whether to give him a visa.

The government here accused the Reagan administration of "increasing the tensions that already exist between the two countries." The flap comes within a month of two other diplomatic flare-ups involving the two nations.

Carlos Nunez, president of the Council of State and a member of the nine-man Sandinista National Directorate, had planned to lead a delegation to the United States to study how U.S. elections are organized. Members of the council, the national legislature, are visiting a variety of countries for this purpose before debating a new electoral law before the end of the year.

The council issued a three-page press release saying that Nunez had applied for a visa Monday to leave today. It said Ambassador Anthony Quainton had said that the State Department was studying whether to grant the visa and that the department recommended that the visit be postponed until next month.

Nunez then canceled the delegation's trip, giving as his reason that Nicaraguans should be able "to decide on their own when to visit a country with which we maintain diplomatic relations," the statement said.

The State Department had said yesterday that it was "seriously considering" whether to grant the visa but was taking into account difficulties at the start of the month when Assistant Secretary of State Langhorne A. (Tony) Motley canceled a visit to Nicaragua at the last minute. There also were delays last month in granting two visas requested by Nicaragua's influential Interior Minister Tomas Borge, although ultimately Borge was told that he could get a visa if he applied again.