Abbas and his Fatah movement, which controls parliament, are wrangling over the method by which the new legislature will be chosen.
Under the new electoral law passed on Wednesday, two-thirds of the legislators would be chosen in district voting, but Abbas wants all lawmakers to be chosen from party slates.
The measure was passed by a 35-20 margin, with one abstention and 28 lawmakers not being present.
Parliament Speaker Rauhi Fattouh said Abbas informed him even before Wednesday's vote that he would veto the legislation.
The stalemate raises doubts about whether a parliament elected scheduled for 17 July would be held on time.
District voting would increase the chances of the current
legislators to be re-elected. Abbas has argued that a vote according to party lists would increase the prospects of his Fatah to hold off a challenge by the increasingly popular Hamas.
The 84-member legislature could only overturn Abbas' veto with two-thirds of the vote - a majority that supporters of the new electoral law are unlikely to muster.
Legislator Azmi Shuaibi, an independent, said the wrangling could cause the parliament election to be delayed.
"If Abu Mazen does not approve this draft, it could delay the elections for a few weeks for technical reasons," he said.