Most problematic for Abbas is likely to be a Hamas's demand that he approve the Executive Force, a 5,600-strong militia set up by Hamas last year despite the president's objections.
Hamas also wants Abbas to approve the appointment of dozens of Hamas loyalists to senior civil service positions, Hamad said. Abbas has in the past refused to certify the appointments.
Hamas is also said to be asking Abbas commit to a candidate for the post of interior minister. Hamas proposed two names for the job, but Abbas has said he wants to review more applicants.
There is also disagreement over how many of the five independents to be proposed for the cabinet can be picked by Fatah. Hamas now says Fatah has run out of picks, while Fatah says it has one left.
Hamad said that as a result, Abbas decided to postpone a speech to the nation, which he had planned to deliver on Thursday, before heading to Gaza to meet with Ismail Haniya, the prime minister.
"Palestinians must focus on the end objective and not get sidetracked by destructive actions"
The president "has put off his speech because of the demands that suddenly arose by Hamas leaders," Hamad said.
"He found it difficult to address people while there are difficulties on the road to implementing the agreement."
Abbas still plans to meet Haniya in Gaza on Thursday, to try to work out the problems, he said.
Ghazi Hamad, a Hamas government spokesman, meanwhile, said he was hopeful the that two leaders could resolve the issues.
Last week's power-sharing deal, brokered by Saudi Arabia in Mecca, cleared the way for setting up a Hamas-Fatah coalition.
However, the agreement dealt only with the government's programme and the distribution of cabinet seats, and left many issues unresolved, such as the fate of the Hamas militia.
Relations between the two sides remain tense, after weeks of fighting in Gaza that left scores dead, hundreds wounded and caused millions of dollars in damage.
Abbas's latest troubles with Hamas come at a time when the international community, led by the US and Israel, is still withholding judgment on the emerging coalition deal.
Abbas is to host Condoleezza Rice, the US secretary of state, in Ramallah on Sunday, to be followed a day later by a three-way summit with Ehud Olmert, the Israeli prime minister.
"He found it difficult to address people while there are difficulties on the road to implementing the agreement"
Nimer Hamad, an Abbas-aide
Abbas told senior members of his Fatah movement on Wednesday that he wanted to hear from Rice and Olmert before delivering his speech.
The summit was initially billed as a step towards renewing peace talks, following more than six years of fighting.
However, Israeli officials have said no issues of substance will be discussed at the summit, because Israel wants to learn more about Abbas's agreement with Hamas.