The appeal was issued at the end of a two-day meeting to discuss US President Donald Trump's December 6 recognition of Jerusalem as Israel's capital which has sparked Arab anger.
Trump's decision also to relocate the US embassy to Jerusalem from Tel Aviv triggered deadly clashes in Palestinian territories and was rejected in a non-binding UN General Assembly resolution.
The Palestinians have frozen contacts with the Trump administration over the decision and said the United States can no longer mediate in the Middle East conflict following Trump's decision.
They also asked for an international conference to be held to re-start peace talks between Israel and the Palestinians and the international recognition of a Palestinian state with east Jerusalem as its capital.
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Arab League chief Ahmed Abul Gheit told a news conference the peace process should not remain "within the hands" of one faction alone.
He also singled out the position of the European Union.
On Wednesday, EU diplomatic chief Federica Mogherini had also said the United States was "essential for any process to realistically have a change to succeed".
Palestinian foreign minister Riyad al-Malki told reporters in Cairo that the "old mechanism has ceased to exist and is history".
"It will not bother us should the United States be part of the (new) mechanism," he added.
Israel occupied east Jerusalem and the West Bank in the 1967 Six-Day War and later annexed east Jerusalem in a move never recognised by the international community.
The city's status is among the most contentious issues in the Israeli-Palestinian conflict.
Israel claims all of Jerusalem as its united capital, while the Palestinians see the eastern sector as the capital of their future state.