Switzerland is part of a group of countries hoping to mediate in a row over reform of the United Nations Security Council.
Meetings are due to take place in New York this weekend to discuss three different proposals.
Switzerland, Sweden, the Netherlands and New Zealand had joined forces and were hoping to win the two-thirds majority needed, said Peter Maurer, the Swiss ambassador to the UN, in New York on Friday.
The proposals include the right to block Security Council decision by a veto vote, the decision-making process and a regular review of the make-up of the council.
There are three proposals under discussion at the UN headquarters in New York.
Germany, Japan, Brazil and India, known as G4, have officially presented their joint plan at the UN General Assembly.
Two other proposals have been drafted by the African Union and by a group of countries, led by Italy, Pakistan and Mexico.
Search for compromise
But the plan by African states to add a total of 11 new members to the Security Council members, including six with a veto right - is not considered acceptable.
The G4 group for its part wants to extend the Council by ten new states, six permanent members and four rotating ones, but none would receive a veto right.
A third proposal aims to just add ten rotating member states to the body.
Reports say the United States, China and Russia are opposed to all three drafts.
Switzerland has come out against proposals to increase the number of countries which have a veto right.
Last month, Maurer called for key elements of a draft document on reforms of the Security Council to be more specific.
Addressing the UN General Assembly he said reforms could be achieved irrespective of the Council’s future size and structure.
The Security Council is currently made of 15 members, including five permanent members with a veto right – US, China, Russia, France and Britain.
The other ten members are chosen on a rotating basis for a two-year term by the UN General Assembly, which is due to meet in September.
swissinfo with agencies
The Swiss electorate approved UN membership in a nationwide ballot in March 2002.
Switzerland officially joined the world body in September 2002.
Previously, Switzerland held observer status and was a member of various UN agencies.
Switzerland, Sweden, the Netherlands and New Zealand aim to mediate in a dispute over reforms of the UN Security Council.
The proposals include working methods of the Council, a veto right and a review of membership rules.