The joint statement said the shedding of "Palestinian blood" should be "prohibited as sin", in reference to fierce infighting between Hamas and Fatah armed factions.
After being delayed for a day due to a dispute between the two sides, the talks began on Sunday evening.
According to Izzat al-Rishq, an aide to Meshaal, the talks were not expected to result in a dramatic breakthrough between the two sides, who for months have struggled to form a national unity government composed of both Fatah and Hamas members.
Before the meeting, al-Rishq said: "The main difference on the government's manifesto persists. The meeting will convene to affirm that the two sides are committed to continue dialogue and reject the use of violence and spilling of Palestinian blood."
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.
Haniya told reporters in Gaza: "Ninety per cent of the issues have been agreed upon. The remaining issues include those relating to the political agenda and key ministries.
"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."
Initially 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.
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