Netanyahu did not specify what "steps" Israel could take, but Israeli legal experts have said that if the Palestinians were to move forward on their own then Israel could cancel interim peace accords.
"Israel could say there has been such a gross and major violation that the agreement itself is no longer in force," Robbie Sabel, a former legal adviser to Israel's foreign ministry, told The Associated Press news agency.
Interim accords agreed by the two sides set up a system of interlocking administrations that falls far short of peaceful relations but brings some order to issues like Palestinian imports and exports, tax collection, utilities and security co-operation.
The Palestinian Authority, which is led by Mahmoud Abbas, the Palestinian president, is itself is a product of the interim accords.
Saeb Erekat, the chief Palestinian negotiator, said that the Palestinians had decided to turn to the UN due to frustration at the lack of progress peace talks, which have been stalled since Israel launched 22-day offensive in Gaza last December.
"Now is our defining moment. We went into this peace process in order to achieve a two-state solution," the Associated Press news agency quoted him as saying.
"The endgame is to tell the Israelis that now the international community has recognised the two-state solution on the '67 borders."
Israel captured and occupied larges areas of the West Bank, Gaza Strip and East Jerusalem after the 1967 Middle East war, and the Palestinians want to form their state based on the borders agreed by a ceasefire before then.
"They are not looking for a unilateral declaration of independence, they have already done that on November 15, 1988," Al Jazeera's Nour Odeh, reporting from Ramallah, said.
"What they want is something a lot more concrete," she said.
"They know it won't immediately result in the withdrawal of Israeli occupation troops from their territory, but they want the Israelis to stand in front of an international collective will that says this is what needs to be done in order for peace to be realised."
Barack Obama, the US president, has been trying to restart talks between Abbas and Netanyahu since the US leader took office in January.
"The US and Israel have avoided the Security Council for more than 16 years. To go back to it today would be a major shift"
Al Jazeera's senior political analyst
But the efforts have been hindered by the issue of illegal Israeli settlement construction in the occupied West Bank. Abbas has demanded a freeze in the construction before the resumption of negotiations.
Mohammed Dahlan, a senior official in Abbas's Fatah faction, said on Sunday that the UN initiative would be "a real test of the intentions of the international community".
"We are now leading a diplomatic battle," he said. "If the American administration does not agree, that will be another setback."
If the Security Council does not approve the measure, Dahlan said other options include a unilateral declaration of statehood and "popular, comprehensive resistance against settlement and the occupation".
Salam Fayyad, the Palestinian prime minister, who in June set a goal of establishing the institutions of a state within two years, said it was time for the international community to take responsibility for "the mission of ending the occupation".
"This is the responsibility of the international community and when we talk about that and international law, of course we are talking about the United Nations," he said in Ramallah.
Marwan Bishara, Al Jazeera's senior political analyst, said: "Everyone knows this will not go to the Security Council without the green light from the US.
"If the US gives the green light, it means the relations between the US and Israel are in trouble.
"The US and Israel have avoided the Security Council for more than 16 years. To go back to it today, would be a major shift, a game changer in the diplomatic process.
"All Palestinians would be quite excited. Everyone, on all various levels, feels betrayed by a process that delivered not much after 16 years and seven agreements with the Israelis while quadrupling the illegal Israeli settlements."
Nimr Hamad, an adviser to Abbas, said the Palestinian president would travel to Cairo on Wednesday to discuss the plan with Hosni Mubarak, his Egyptian counterpart.