"The ball is in the Israeli court," he said.
"We are waiting to see if they are serious. If they are serious they have to deal with the situation in the occupied territories in a different way."
Jerusalem, which the Palestinians want as a joint capital for a future state, has been a particular point of focus for delegates.
Calls for resistance
But Arab leaders failed to reach consensus on whether the Palestinians should resume stalled talks with Israel.
Leaders rejected pressure from Syria and Libya on the Palestinians to abandon talks with Israel and resume armed resistance.
"The Arab peace initiative is a serious move. If we withdraw it, what will be the Arab stance after that," Moussa said.
Nabil Abu Rudaina, a senior Abbas aide, also dismissed the pressure. "Let us be realistic. We will not follow those who have special agendas," he told Al Jazeera.
"We are ready for any Arab option. If they want to go to war, let them declare that and mobilise their armies and their people and we will follow suit."
The Palestinians pulled out of the peace talks in reaction to Israel's announcement it would build 1,600 settlements on occupied land.
Mahmoud Abbas, the Palestinian president, has ruled out taking part in the talks unless Israel stops building settlements.
But Israel has rejected the calls.
Danny Ayalon, Israel's deputy foreign minister, said the country has a "legal right" to build in Jerusalem.
"We say strongly and firmly that we have a legal right to build in Jerusalem and those that seek to enshrine the 1949 Armistice Lines, the so-called Green Line, as a border, have not understood history nor legal precedence," he said.
"We call on the Palestinian Authority to cease living in delusions of forcing Israel to the pre-1967 lines and to come and join us at the negotiation table without preconditions."
Moussa, who said a day earlier that continued Israeli settlement building would end efforts to revive the stalled peace process, reiterated the warning on Sunday.
"Within the next few weeks we have to decide what to do: whether to continue with the negotiations or to completely shift course," he said.
"If we find out that Israel is not leaving an opportunity to build two states, we are investigating the possibility of supporting a one-state solution.
"But such a decision will ... come after serious investigation and study."
The leaders plan to hold an extraordinary meeting in September to discuss issues it was unable to resolve during the just concluded summit.
Al Jazeera's Mike Hanna, reporting from Sirte, said Moussa's statements indicated a call for a new regional reality to counter years of rhetoric.
"He's stating very specifically that in the past there has been lots of rhetoric, lots of talk, but it has not actually confronted what is the reality," he said.
"The reality is - as Arab states see it - continued support for Israel, by the United States in particular, despite the ongoing suffering of the Palestinian people.
Our correspondent said: "Year after year these summits are held and yet the reality on the ground is that the situation is not resolved.
"Amr Moussa is acknowledging this, probably publicly for the first time - saying, 'Yes there is an element of truth behind this, we have been talking for too long'."
Our correspondent said the leaders also discussed exploring closer relations between the Arab League and Iran, possibly through a forum that would include Turkey.
Leaders at the summit also discussed Iraq and the state of security in the country following its recent elections.
Al Jazeera's Anita McNaught, reporting from Baghdad, said the summit leaders pointed out that Iraq's security is crucial to the region's stability.
"This election is at a crucial stage," she said.
"If Iraq gets it right, the implications for Iraq's neighbours are very positive. If things dissolve into rancor and violence, the effect will be massive."