But Washington is still insisting that the document must not "create any new international human rights" - which opponents say could also mean abortion.
At a closed-door meeting on Thursday, US ambassador Ellen Sauerbrey announced that the US was dropping part of its proposed amendment relating to abortion and leaving the part on international human rights on the table.
But delegates from the European Union, the African Union, the Mercosur trading bloc in South America, and other countries strongly opposed any amendment to the one-page declaration that reaffirms the landmark platform adopted at the 1995 UN women's conference in Beijing to achieve equality of the sexes.
Abortion in spotlight
Nilcea Freire, Brazil's minister of state for women's affairs, said not a single country supported the revised US amendment, and every speaker insisted that the declaration be left untouched and simply reaffirm the language of Beijing, "nothing more".
The wording of the declaration has taken the spotlight at the two-week high-level review of the Beijing platform, angering many of the 130 governments and 6000 representatives of women's and human rights organisations.
The US says the declaration is not
They had been hoping to focus on the obstacles to women's equality in the economy, the family, education and political life - not on the abortion issue.
Hoping to avoid controversy, the Commission on the Status of Women, which organised the meeting, had drafted a one-page declaration that would have nations reaffirm the Beijing platform and pledge to accelerate its implementation.
National sovereignty issue
But Sauerbrey said the major US concern has been to establish a principle that the Beijing platform "is not a legally binding document, that issues such as abortion are issues of national consensus, national policy".
After Thursday's debate, she said she was going to report the reaction of delegates to Washington and await instructions.
"Whatever happens in the next day or two, I think one of the things that has been very clearly established that should give a lot of comfort to concerned Americans is that virtually every country said we interpret it the same as you - we interpret that these are issues of national sovereignty," Sauerbrey said.
"Basically, this is irrefutable evidence that the United States is determined to roll back Beijing"
Adrienne Germain, International Women's Health Coalition chief
"If we can establish that clearly, we will feel that we have established something constructive," she said.
Asked about the US failure to get support from a single country, Sauerbrey said "there's just an awful lot of peer pressure" and countries that indicated they would support the US position were too "intimidated" to stand up.
June Zeitlin, executive director of the Women's Environment and Development Organisation, said dropping the reference to abortion was "a good first step" and the US should now withdraw the entire amendment "and join the women of the world and the global consensus to unequivocally reaffirm the Beijing platform".
Adrienne Germain, president of the International Women's Health Coalition, called the shortened US amendment "disingenuous".
"By keeping the phrase 'no new international human rights', they can then turn around and say, of course no right to abortion," she said.
Germain said the US has been faxing governments seeking support for the amendment and asking governments to make an explanation regardless of the outcome which would say that "sexual rights are objectionable" that Beijing does not create a right to abortion, and that language on adolescents' right to privacy on sexual health matters must be balanced with parental rights.
"Basically, this is irrefutable evidence that the US is determined to roll back Beijing," she said.