"You're not alone on this," Abdullah said in the interview when asked about Israeli concerns that the power-sharing deal between Hamas and Mahmoud Abbas, the Palestinian president and Fatah leader, fails to meet the Quartet's demands.
The Quartet of Middle East peace negotiators comprise the US, the EU, Russia and the UN.
"There's international common ground - not just Western but also Arab and to an extent Muslim - that believe that there have to be certain criteria that the new government has to accept if we're going to move the process forward," Abdullah said.
Jordan has openly expressed support for Abbas, who is backed by the west, and called for a renewal of peace talks.
Jordanian officials have privately supported US-led efforts to isolate the Hamas government that took power after winning the January 2006 elections, unless it embraced Middle East peace moves.
While the unity government agreement contained a promise to "respect" previous Israeli-Palestinian agreements, it fell short of what the Quartet wants.
"The land of Israel belongs to both Jews and Palestinians - as long as there are people who reject this fact, the conflict will never be solved"
Iskander, Boston, US
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"It's not just ... the international players, but also the Arab countries are also expecting the new Palestinian government to adhere to the policies that we have set out in the Quartet, and in the Arab Quartet also," Abdullah said, referring to Jordan, Saudi Arabia, Egypt and the United Arab Emirates.
King Abdullah said Abbas should be given "the mandate to start negotiations with the Israelis", and the new government should be in "full compliance with the Arab Accord as well as international commitments".
The Arab initiative, launched in 2002, would trade diplomatic recognition for Israel's withdrawal from land it occupied in the 1967 Arab-Israeli war.
Abdullah said the initiative was being re-launched and could draw broader support from Muslim countries around the world.
The unity government deal has widened rifts within the Quartet over how to deal with the Palestinian government.
"I think the circumstances in the Middle East have changed so much so that really this is our last opportunity"
King Abdullah II of Jordan
Washington wants to shun the new government to keep pressure on Hamas.
Russia and some European states favour a softer line.
Khaled Meshaal, leader of Hamas, said on Friday that several European states had pledged to send money to the new government, though he offered no details.
In the interview, Abdullah said time was running out to revive the long-stalled peace process.
"I think the circumstances in the Middle East have changed so much so that really this is our last opportunity," he said.
Condoleezza Rice, the US secretary of state, held a three-way meeting on Monday with Abbas and Ehud Olmert, Israel's prime minister. But it appeared to do little to jumpstart peace-making.