Human rights groups have criticised Israeli armed forces for firing on unarmed protesters at borders with the Palestinian territories, Syria and Lebanon.
The BBC says that at least 12 people have died and dozens more have been injured.
Israel has justified the actions, claiming that thousands of Palestinian supporters from Syria entered the Golan Heights. But critics respond that public protest against occupation and denial of rights is legitimate and inevitable.
On Sunday Palestinians were marking the 'Nakba' or 'Catastrophe', their term for the founding of the Israeli state in 1948, while many Israelis were celebrating their statehood.
On the sixtieth anniversary of the state of Israel, three years ago, Christians and faith leaders, including Archbishop Emeritus Desmond Tutu, issued a statement, signed and circulated by Ekklesia and others, calling for rights and national autonomy for Palestinians, as well as recognition and peace for Israelis - arguing that a just-peace is in the interests of all.
Hundreds of thousands of Palestinians fled or were forced out of their homes in fighting after the creation of the state of Israel, a fact which some supporters of the country refuse to acknowledge and act upon. This in turn has led to anti-Israel bitterness and hostility.
Responding in a televised address to the violence on 15 May 2011, Israeli Prime Minister Benjamin Netanyahu said he hoped "calm and quiet will quickly return, but let nobody be mistaken, we are determined to defend our borders and sovereignty".
Later on that day, security forces in the Egyptian capital Cairo fired warning shots and tear gas to break up protests outside the Israeli embassy.
UN Secretary-General Ban Ki-moon has urged all sides to show "utmost responsibility".
He said there was an "unsustainable status quo in the Arab-Israeli conflict, which is only thrown into sharper relief by the profound political changes now under way in the region".
The UN chief called for a renewed effort to reach comprehensive peace in the region.
Reuters reports that repeats of the 'Nakba Day' marches looked likely, given the Palestinians' campaign to corner Israel at the United Nations' General Assembly in September 2011, by declaring independence should peace remain stalled.