Abbas, in a presidential decree, had earlier accused Said Siyam, the interior minister who nominally heads some of the Palestinian security forces, of acting illegally by conceiving the new force and appointing Jamal Abu Samhadana to lead it.
Government spokesman Ghazi Hamad denied that allegation.
"The decision of the interior minister conformed with the law ... which gives the minister the authority to take the necessary decisions to guarantee security," Hamad said.
"The aim of the decision was to support and strengthen the efforts of the police, and not to replace the police."
Abbas issued a presidential decree on Friday vetoing decisions made on Thursday by Siyam.
In a letter to Ismail Haniya, prime minister of the Hamas administration, Abbas said "we have learned through the media that the interior minister issued decisions violating the law".
"All the officers, soldiers and security personnel are asked not to abide by these decisions and to consider them non-existent."
Siyam's decision to appoint Jamal Abu Samhadana – a founder member of the Popular Resistance Committees who has survived at least one assassination attempt by Israel – was seen as a challenge to Abbas's authority.
The new force was to be made up of militants from different factions and would have been controlled by the interior ministry.
Under Palestinian basic law, the president has the power to veto government appointments.
The row over the appointment threatens to widen the rift between Abbas and Hamas.
Both have been wrangling over control of the levers of power within the Palestinian Authority since the Islamist group won January's parliamentary elections.