"UN Watch's draft resolution to remove (Richard) Falk has been published by the United Nations as an official document and will be put before the (Human Rights) Council when he addresses it tomorrow," the group said in a statement.
US ambassador to the Human Rights Council, Eileen Chamberlain Donahoe, also called for Falk's departure in a statement Friday.
The calls came after the outspoken expert on the rights situation in the Palestinian territories published a report in which he urged the council to investigate UN Watch, which he described as "a pro-Israel lobbying organisation accredited as an NGO."
In his report, which he is set to present to the rights council in Geneva early tomorrow, Falk accused UN Watch of launching "a smear campaign" against him, charging it "has issued a series of defamatory attacks demeaning his character, repeatedly distorting his views on potentially inflammatory issues."
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He called on the 47-member rights body to investigate UN Watch "to determine whether it qualifies as an independent organisation that operations ... And is not indirectly sponsored by the government of Israel."
Falk, a Princeton University international law professor who has labelled Israel's 2008 offensive against Gaza as "war crimes", also met harsh US and Israeli criticism after he last year urged a boycott of companies helping Israel's settlement expansion in the Palestinian territories.
The report he is set to present tomorrow takes Israel to task for a long line of alleged abuses, many linked to its "illegal blockade of Gaza," an area likened to "a large open-air prison in which the inmates control the interior while the guards control the perimeter.