Political analyst Marwan Beshara told Al Jazeera just before the speech started at midday: "There is a clash of wills between Hamas and Fatah. Abbas needs to be presidential.
"Even if Fatah wins an election ... you cannot win a majority and govern because Palestine is occupied."
Analysts say an annocunment by Abbas for ealry elections would be a bold move.
Khalil al-Hayya, the head of Hamas's faction in parliament, has said Hamas would not agree to holding early elections or a referendum on the issue, but he did not say what Hamas would do if Abbas made such an announcement on Satruday.
Tensions are running high in Gaza after months of failed talks aimed at forming a unity government between the ruling Hamas Islamist faction and Abbas's once dominant Fatah.
At a rally on Friday to celebrate Hamas's 19th anniversary, al-Hayya told 100,000 Hamas supporters: "What a war Mahmoud Abbas you are launching, first against God, and then against Hamas."
Ismail Haniya, the prime minister and leader of Hamas, made an appeal at the rally for "national unity" but stopped short of explicitly calling for calm.
Saeb Erekat, a senior aide to Abbas, told Reuters that president Abbas was "leaning towards" early elections.
He said: "The president's choice is between bullets and ballots. He will choose ballots. Ballots are the only way to avoid the prospect of a civil war."
On Friday, at least 32 Hamas supporters in Ramallah were wounded by gunfire and several were left in a critical condition, hospital officials said.
Fighting started in the West Bank but spread to Gaza where Hamas and Fatah forces exchanged fire on the streets.
|Thousands of supporters attended a rally|
celebrating Hamas 19th anniversary
Dressed in riot gear, the Fatah-dominated forces used clubs and rifle-butts to beat back Hamas demonstrators before the shooting broke out.
On Thursday, security forces fired on a convoy carrying Haniya as it crossed into Gaza.
One bodyguard was killed and several other people injured.
Ismail Rudwan, a Hamas spokesman, accused Mohammed Dahlan, a Fatah regional commander and legislator, of being behind the attack on Haniya's convoy in Rafah.
Dahlan rejected the allegation, accusing Hamas of a "cover-up" over unidentified fighters who shot dead three children of an intelligence official loyal to Abbas outside their school.
Haniya has condemned the killings and the government said on Friday it would investigate the incident.