Key Third World nations split here today over whether to accept President Reagan's conditions for starting global negotiations aimed at solving the economic woes of the nonindustrialized South.

A group of nations led by Cuba and Algeria insisted at a three-day "South-South dialogue" called by Prime Minister Indira Gandhi that the Third World should reject the Reagan conditions, especially one that would ban discussions on giving the have-not nations more power in international lending organizations such as the World Bank and International Monetary Fund.

Other nations, including Pakistan, urged a quick start to economic talks between all the nations of the world, even if the Third World is forced to compromise, in the hope of pushing the industrialized North, especially the United States, into changing its stance.

In an effort to bridge that gap, Indian delegate Romesh Bhandari characterized the position of the so-called New Delhi Consultation of 44 Third World Nations as being both "firm and flexible."

He said that meant remaining firm in its commitment to global negotiations while being flexible in its approach and strategy. Nonetheless, the more than 120 developing countries who make up the so-called Group of 77 in the United Nations will have to evolve a common strategy soon to get ready for next month's General Assembly session, which is expected to discuss the call for global negotiations.

Furthermore, there appears to be little chance for change in the position of the Reagan administration. American diplomats around the world are known to have received repeated cables from Washington reminding them that the U.S. position is firm, set at the presidential level and not subject to negotiations.

Previously there had been great hesitation by the United States toward accepting the underdeveloped South's call for global negotiations, which Washington feared would lead only to the richer nations of the West being flogged with rhetoric by the more numerous and populous Third World countries.

Thus even Reagan's limited acceptance of global negotiations was considered by some to be a major shift in U.S. policy.

In a briefing tonight, Indian delegate Bhandari acknowledged the differences among the key Third World participants and said the major split "in which we cannot find common ground" concerned changes in the structure of agencies such as the World Bank and IMF.

Major European nations considered more favorable to the South's position than the Reagan administration have urged the Third World to accept the U.S. conditions to get the talks started.

India, which over the years has been the largest recipient of World Bank funds, was reported to have attempted to soft-pedal the debate over greater Third World power in the international institutions.

Nonetheless, India took the lead in attacking "the negative trend" of cutbacks in low-interest loans from the World Bank--an area in which New Delhi has begun to feel the pinch.

The "South-South dialogue" here also criticized "outmoded concepts such as graduation" that would make the better-off nations of the Third World such as India eligible for only higher interest World Bank loans; the stress on the use of private capital for development projects; cutbacks in foreign aid, and the use of high interest rates to improve the economies of the industrialized world.

Although the United States was not mentioned, the first three are acknowledged Reagan policies.