The Syrian office of Hamas also wanted an explanation for the statements about "common enemies" facing Jordan and Israel, ascribed to Abdullah by Haaretz's sources.
The Palestinian Islamic resistance group said the right of return is "sacred" and that no one has the authority to give it up.
The report in Haaretz cited unidentified members of the Israeli legislators' delegation.
A member of the Israeli delegation told The Associated Press on Saturday that Abdullah's comments were accurately reported by the Israeli daily.
He gave no further details.
Besides Hamas, the Popular Front for the Liberation of Palestine-General Command (PFLP-GC), another Syria-based Palestinian faction, denounced the remarks attributed by the Haaretz report to Abdullah, saying they reflected a "top alliance with the Zionist enemy".
Al Jazeera quoted a PFLP-GC statement as saying that Palestine is not a land to be subjected to a "marketplace for settlement".
For its part, Islamic Jihad said that the Jordanian royal's purported remarks are tantamount to inviting the Palestinian people to give up the tenets and principles for which they have struggled for decades.
The group said the right of return is a legal right and an inalienable human right not open to compromise or procrastination, and the inability to recover it does not amount to forgoing it.
Jordan has denounced the Haaretz report.
Amjad al-Adhaylah, head of information department at the royal palace in Amman, said it caused "flagrant harm to Jordan and its leadership and jeopardised the serious effort to aid the Palestinian people".
Jordan "has the right to defend the rights of its citizens who are refugees", he said in a statement.
The kingdom hosts the largest number of Palestinian refugees in the Middle East, many of whom have Jordanian citizenship.
Al-Adhaylah said: "The compensation choice comes within the framework of solving the Palestinian refugee problem but won't be the only solution."
Al Jazeera tapes seized
In another development, Jordanian authorities have confiscated the tapes of an interview given by Prince Hassan Bin Talal, uncle of the king and a former heir to the throne, to Ghassan ben Jeddou, Al Jazeera's Beirut bureau chief, for the channel's Open Dialogue programme.
On the tape, Hassan criticised US policies in the Middle East as "destructive" and cited US reports that a national security adviser in Saudi Arabia was financing Sunni fighters to fight Hezbollah, the Iranian-backed Shia Lebanese group.
Nasser Judeh, the chief Jordanian government spokesman, confirmed the confiscation but said it had nothing to do with the content of the interview.
Ben Jeddou said Jordanian authorities informed Al Jazeera's office in Amman that the seizure was "an official measure by Jordanian authorities" and that they have "no problem with Al Jazeera".
In other news, Mahmoud Abbas, the Palestinian president, said on Saturday that European governments have offered positive responses to his campaign for an end to EU economic sanctions on the Palestinian government.
|Abbas, right, and Ismail Haniya of Hamas are|
battling a financial blockade [Reuters]
On a three-day visit to Athens, the Greek capital, he said: "We received a positive response from everyone and hope soon to see this materialising in practice.
"We call for the lifting of the embargo, as its continuation can only lead to the increase of extremism.
"We condemn extremism."
The financial blockade was imposed on the Palestinian Authority after Hamas swept to power in the January 2006 elections.
Abbas' tour has included France, Sweden, Poland and Bulgaria. He is also due to visit Italy and Switzerland.
Earlier this month, the new Palestinian finance minister said that his government needed $1.33bn in international support "to get back on its feet".