Speaking in an interview with AFP, Abbas criticised what he said was insufficent action from US President Barack Obama's administration while also firmly backing a French initiative to hold an international peace conference this summer.
Abbas spoke ahead of a tour beginning today that will take him to Turkey, France, Russia, Germany and New York, where the Palestinians are discussing a UN draft resolution condemning Israeli settlements in the occupied West Bank.
"The Security Council is a very important subject because it has now become urgent due to settlement activities and because Israel has not stopped these activities," Abbas said late Monday at his office in Ramallah.
Settlement construction in the West Bank "is something that has seriously jeopardised the two-state project."
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The United States has repeatedly vetoed resolutions opposed by Israel at the UN Security Council, but the Palestinians are hoping for a change of heart.
He criticised US efforts so far.
"We were expecting from the US administration over the past eight years that it would take positive steps forward to achieve what America believes in, which is the two-state vision," he said.
"Until now, it hasn't happened from the US administration."
Asked whether he was disappointed, he said: "We do not want to use this expression, but we are saying that we were expecting a lot from the US administration and it never happened."
Abbas' two-week tour starts with a summit of the Organisation of Islamic Cooperation in Istanbul and ends in New York.
International attention in recent years has however turned elsewhere, with war raging in Syria and Islamic State group jihadists carrying out attacks.