The US and other nations have urged the UN to ban all forms of human cloning, on the second of two days of debate.
Stem cells from cloned embryos could help with the understanding of diseases
An opposing group of countries want the cloning of human stem cells to be permitted for medical purposes.
The US has been pushing hard for a ban, but the UN is unlikely to vote before the 2 November US election, in which the issue has divided the candidates.
The matter is being discussed at the General Assembly's legal committee, which features all 191 UN members.
Two different resolutions are on the table:
- One, drawn up by Costa Rica and backed by the United States and 60 other countries, calls for a treaty to ban all cloning, which it calls unethical and morally reproachable
Another, drafted by Belgium, would ban cloning humans but allow countries to decide for themselves whether they wanted to ban or permit "therapeutic cloning" for research.
Costa Rica's Foreign Affairs and Worship Minister, Roberto Tovar, said his country was putting forward an initiative for human dignity.
On Friday Kenya, Nigeria and Norway were among the countries on the same side of the argument, the latter citing "respect for the inviolability
However Belgian diplomat Mark Pedsteen said his government's resolution focused on what united, rather than divided, the members.
Sweden and Thailand are among its backers. Sweden argued that "freedom of research is essential, and it must always be carried out within ethical boundaries".
Before the meeting, UN Secretary General Kofi Annan told reporters it was up to member-states to decide - but personally he would back therapeutic cloning.
Last November, the committee narrowly voted to delay considering any treaty for two years but this postponement was subsequently reduced to a year.
It is a high-profile issue in the upcoming US presidential election.
President George W Bush opposes all cloning while his Democratic challenger, John Kerry, backs stem cell research.
South Korea has suggested there should be another year's delay to allow time for a UN conference on embryonic stem cell research.