The talks in Doha, where Meshaal is based, were hosted by Qatari emir Sheikh Tamim bin Hamad al-Thani, a key backer of the Islamist movement which dominates Gaza, the Gulf state's QNA news agency reported.
A Palestinian delegate told AFP that the talks between the three leaders lasted nearly three hours and were expected to be followed by a two-way meeting between Abbas and Meshaal.
The head of the Palestinian negotiating team at the abortive truce talks, Azzam al-Ahmed, joined the meeting, along with Palestinian Authority security chief Majid Faraj and senior official Saeb Erakat, the official Palestinian news agency WAFA said.
The Hamas armed wing declared the truce efforts over yesterday after Israel carried out an abortive assassination attempt on its leader Mohammed Deif, killing his wife and two of his children.
"There will be no return to talks after today and any move in this direction will never achieve any result," said Ezzedine al-Qassam Brigades spokesman Abu Obeida.
A new Israeli air strike killed three other senior Hamas commanders early today.
The renewed strikes pushed to 2,075 the number of people killed in Gaza since July 8, around three-quarters of them civilians, according to the United Nations.
It is the deadliest confrontation between Israel and Hamas since the second Palestinian intifada, or uprising, between 2000 and 2005.
The Palestinians have been demanding an end to Israel's eight-year blockade of Gaza and the opening of an airport and seaport.
Israel has been demanding the demilitarisation of the territory, something rejected by the Palestinians.