Admission to UNESCO has had no impact on the Palestinians' bid for full UN membership. They would need nine votes out of 15 in the Security Council, but the United States has made clear that it would veto the bid.
Abbas said efforts were continuing to gain full UN membership and admission to other international institutions.
"We are currently holding talks with the parties," he said when asked about the Security Council at a press conference.
"We have not yet asked for a vote but this could happen at any moment. If we don't have a majority, we will repeat our request again and again."
"We intend to address all international organisations," he said, adding: "But we will choose the right time to do this."
The Palestinians were admitted to UNESCO in late October, when its general assembly voted 107-14 to make Palestine its 195th member.
The result angered the United States, Israel's staunch ally, which says the Palestinians must reach a peace agreement with the Jewish state before they can become full members of an international organisation.
Washington immediately suspended its funding to the UN agency, which selects and oversees World Heritage sites and also works in areas from literacy and media freedom to science and environmental issues.
The US cash freeze deprived UNESCO of 22 percent of its budget, leaving a hole of $65 million (49 million euros) this year and a $143 million shortfall for 2012-13.
At the ceremony, UNESCO director general Irina Bokova welcomed the new member, saying she hoped the admission of the Palestinians would be a step toward peace with Israel.
"A solution with two states living in peace and security has been long awaited," she said. "I'd like to believe that this admission to UNESCO is a chance to show that peace is also built through education and culture."
But Israel denounced the flag-raising, with Prime Minister Benjamin Netanyahu's spokesman Mark Regev saying Palestinian membership in UNESCO did nothing to further peace efforts.
"The ceremonial raising of a flag will do nothing whatsoever to advance the cause of peace and reconciliation," he told AFP in Jerusalem.
"The only way to do that is through direct peace talks. Israel proposed this week restarting direct talks ... but unfortunately the Palestinians once again responded that they do not agree to return to the negotiating table."
Israel took its own retaliatory measures after the UNESCO admission, by deciding to accelerate settlements in occupied East Jerusalem and the West Bank and freezing the transfer of funds to the Palestinian Authority.
Every month, Israel transfers tens of millions of dollars in customs duties on Palestinian-bound goods that transit through Israeli ports, but it often freezes them as a punitive measure during disagreements.
Faced with international criticism, Israel later lifted its freeze on the funds, which represent a large chunk of the Palestinian Authority's budget.
Abbas said the Palestinians were willing to return to talks but not as long as Israel's "colonisation" through settlements continued.
"There is a will for peace from our side," he said.
In Ramallah, resident Mahmud Rimawi said he was proud the flag was flying at UNESCO.
"The world needs to know there is a Palestinian people, a Palestinian cause. I hope the next step will be (full membership in) the UN," the 55-year-old said.
Abbas was to meet French President Nicolas Sarkozy later Tuesday and then travel on to Brussels.
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