US President Barack Obama is ending his visit to the Middle East with a trip to the famous ruins of the ancient city of Petra in Jordan.The diplomatic part of his visit ended on Friday when he met King Abdullah and pledged an additional $200m (£131m) to help Syrian refugees in Jordan. Correspondents say his four-day visit has yielded mixed results.He brokered an Israeli rapprochement with Turkey but there was little progress on the Palestinian issue.The BBC’s North America editor, Mark Mardell, says the American leader’s clear warmth towards Israel comes at a price, and many in the Arab world will feel let down.Yet, our editor adds, he brought a subtle message to young Israelis that every people deserves freedom and a land of its own. Israeli apology Mr Obama’s Marine One helicopter touched down near Petra after an hour-long flight from the Jordanian capital, Amman.Neither cynics nor partisans fully understand the magnitude of Mr Obama’s ambition - nor the length of his game”The site of the ancient city, which is carved into rose-red stone, dates back 2,000 years and is Jordan’s top tourist attraction, drawing more than half a million visitors each year.Most of the president’s time in the Middle East was spent in Israel where he held several meetings with Prime Minister Benjamin Netanyahu.A highlight of the visit came when Mr Netanyahu apologised to Turkey for "any errors that could have led to loss of life” during the 2010 commando raid on an aid flotilla that tried to breach the Gaza blockade.He also agreed to compensate the families of the nine Turkish activists who were killed.Turkish Prime Minister Recep Tayyip Erdogan’s office said he had accepted the apology, "in the name of the Turkish people”.Mr Obama also briefly visited Ramallah in the West Bank to meet Mahmoud Abbas, the president of the Palestinian Authority.He urged Palestinians to drop their demands for a freeze in Israeli settlement-building as a precondition for peace talks.However, a spokesman for Mr Abbas said the Palestinian leader had told Mr Obama the precondition remained in place.Speaking to an audience of young Israelis in Jerusalem, Mr Obama praised Jewish nationhood before turning the argument around by stressing the need for Palestinians to share these same values of self-determination and justice."It is not fair that a Palestinian child cannot grow up in a state of her own living their entire lives with the presence of a foreign army that controls the movements of her parents every single day,” Mr Obama said.The US leader is due to return to Washington later on Saturday.Agencies