Netanyahu's quick trip to neighboring Jordan came after U.S.  President Barack Obama's envoy also tried to press the Palestinians to restart direct peace negotiations with Israel.
 

Netanyahu's office said he had two hours of talks with King Abdullah II, emphasizing "the need to ensure direct, serious and effective negotiations" toward "two states for two peoples."
 

Palestinians insist that before upgrading indirect talks mediated by the envoy, George Mitchell, Israel must halt all settlement construction and accept the concept of a Palestinian state in all of the West Bank, Gaza Strip and east Jerusalem, with some territorial adjustments.
 

Netanyahu insists that talks must resume without preconditions.
 

A Royal Palace statement from Amman said King Abdullah and Netanyahu discussed ways for starting "serious and effective" direct Palestinian-Israeli negotiations. It did not elaborate.
 

The palace statement said Abdullah asked Netanyahu to "make use of the opportunity available now to achieve peace, which constitutes a strategic interest for all sides involved."
 

In a speech after returning home, Netanyahu praised Abdullah's involvement. "We talked about promoting peace between Israel and the Palestinians and in the whole region," Netanyahu said. "I welcome Jordan's efforts for progress toward these goals."
 

"The formula for peace is a demilitarized Palestinian state that recognizes the Jewish state," he said, after demanding security arrangements without giving details.
 

Jordan and Egypt are the only Arab nations that have full peace treaties with Israel. Relations between Jordan and Israel have cooled as the Israel-Palestinian peace process drags on with no visible results.

Palestinian Authority President Mahmoud Abbas also in Jordan, met King Abdullah II on Monday.
 

Abbas' chief negotiator, Saeb Erekat, challenged Netanyahu, saying the "key to direct negotiations lies in the Israeli prime minister's hands."
 

He said Netanyahu must accept the obligations of previous Israeli governments concerning the borders of a future Palestinian state and stopping settlement construction — which should be considered terms of references for direct talks to start.
 

"These are not Palestinian conditions, they are Israeli obligations which must be met," he said.

(AP contributed to this report)