Farouq al-Shara, the Syrian vice-president, reportedly held separate talks with Abbas and Meshaal on Sunday.
After Abbas met al-Shara, Erekat told journalists: "Our message is forbidding infighting, stopping instigation and the formation of a national unity government."
Earlier, Moussa Abu Marzouk, deputy head of the Hamas' political bureau in Syria, said: "the possibility of a meeting today has become non-existent.
The talks had been postponed on Saturday after the two sides failed to reach an agreement on the proposed unity government and then appeared to have been cancelled just hours before Erekat made his announcement.
Marzouk told Al Jazeera's correspondent in Damascus, Zeina Khodr, that the two sides had disagreed over policy recognition.
Abbas wants Hamas to recognise all past political agreements signed by the Palestinian Liberation Organisation (PLO) and Israel. Hamas only accepts policies it agrees with.
Ismail Haniya, the Palestinian prime minister, said on Sunday that Hamas was not willing to recognise Israel despite offering a long-term truce with the Jewish state.
"We accept a Palestinian state on the lands [Israel] occupied in 1967, but in return for a long-term truce and not recognition," he said.
He also said there would be no new crisis even if Abbas and Meshaal failed to reach a full agreement at the meeting.
"Ninety per cent of the issues have been agreed upon. The remaining issues include those relating to the political agenda and key ministries," Haniya told reporters in Gaza.
"With a more focused and comprehensive dialogue, we will be able to reach final understandings that will prepare the ground for the formation of a national unity government," he added.
Abbas, who leads the opposition Fatah party, was to have met Meshaal in an attempt to end growing conflict between the two rival groups.
The meeting was to have followed talks between Abbas and Bashar al-Assad, the Syrian president.
Abbas and Meshaal had been expected to discuss the names of the ministers for interior, finance and foreign affairs in a proposed Palestinian unity government.
Fatah and Hamas have tried for months to agree on a national unity government, in hope of ending a boycott by the United States and the European Union and in order to present a united front towards Israel.
Washington and Brussels consider Hamas to be a terrorist group and suspended direct financial aid to the Palestinians because the movement refuses to renounce violence or recognise Israel.
Tensions between the two factions, which had already claimed a number of lives, boiled over in the Gaza Strip in December, killing more than 30 people in that month alone.
However, violence has tapered off in the past couple of weeks.
Clashes last month began after Abbas called for early elections as a way of resolving the standoff with Hamas, which rejected the move.
Meeting with Syrian leader
Abbas's meeting with al-Assad reportedly ended amicably with the Syrian leader reaffirming his commitment to the Palestinian cause.
Briefing reporters in Damascus, Nabil Amir, Abbas's spokesman, said the two leaders had an "amicable and very frank" discussion that focused on "Palestinian issues in detail and the regional situation".
He reported that al-Assad had told Abbas that he was "attached to Palestinian national unity and ready to support anything that could help reinforce it, as well as efforts to find an adequate solution to the Palestinian problem."
Syria hosts the exiled leadership of a number of Palestinian groups and could exert considerable influence over Hamas. Meshaal moved to Syria from Jordan after an Israeli assassination attempt in 1997.
Source: Al Jazeera and agencies