A high vote could boost Abbas' standing.
"If there is a poor turnout, a poor vote, the radicals gain," said India's U.N. Ambassador Hardeep Singh Puri.
The Palestinians turned to the General Assembly after the United States announced it would veto their bid last fall for full U.N. membership until there is a peace deal with Israel.
Following last year's move by the Palestinians to join the U.N. cultural agency UNESCO, the United States withheld funds from the organization, which amount to 22 percent of its budget. The U.S. also withheld money from the Palestinians.