Envoys from the Middle East Quartet met in Brussels on Friday amid calls from the Palestinians to step up action to halt continuing Israeli settlement activity.

Officials from the United States, United Nations, European Union and Russia gathered "to consult as they routinely do over the phone as well", said a spokesman for EU foreign policy chief Catherine Ashton.

But on the eve of the meeting chief Palestinian negotiator Saeb Erekat called on the group "to restore credibility and relevance to its role" by taking firm action to stop Israeli settlement construction.

"Since the Quartet was created, the Israeli settler population in the occupied Palestinian territory increased by one fifth," he said in a statement.

"Yet the Quartet has not taken any concrete measure to stop this alarming trend, which the international community unanimously agrees now seriously threatens the prospects of the two-state solution."

The Palestinians say there can be no resumption of direct talks while Israel continues its expansion of settlement building in the occupied territories.

Diplomatic sources in Jerusalem told AFP however that Erekat and Israeli negotiator Yitzhak Molho would head to Washington next week for a new round of quiet diplomacy.

While direct peace talks between Israel and the Palestinians remain in deep freeze, high-level officials from both sides have been holding a quiet dialogue on a range of issue, including an exchange of letters between Israeli Prime Minister Benjamin Netanyahu and Palestinian president Mahmud Abbas.

They have also covered a mass Palestinian hunger strike, and a Palestinian request for the transfer of arms from Jordan to Palestinian Authority security forces.

Friday's meeting of Quartet envoys follows April 11 talks in Washington in which the group's top diplomats, or principals, appealed to both sides to build trust in order to revive peace talks frozen since September 2010.