"What is he expecting to achieve when the Americans have no interest in promoting Middle East peace and when the Europeans are still imposing the economic blockade [on the Hamas government]. It is very doubtful he can do anything," said Said, deputy director of al-Ahram Centre for Political and Strategic Studies, a Cairo think tank.
Egypt plays an important role in mediation between Israel and the Palestinians and British officials have said that Blair wants to relay to Abbas, Egyptian and Turkish thoughts on the consequences of any moves he may make to form a government or call elections when he travels to the Palestinians territories.
Blair will travel to Israel, the Palestinian territories and the United Arab Emirates.
Blair sees progress between Israel and the Palestinians as helpful to ending bloodshed in Iraq, where post-invasion conflict has damaged Britain's reputation in the region and eroded the prime minister's popularity at home.
While in Cairo, the British premier also visited the Grand Imam of AL-Azar Dr Mohammed Sayed and religious leaders at the Al-Azar headquarters.
Blair, speaking earlier in Turkey, predicted that Abbas would come up with a way to end a stalemate with Islamist Hamas over forming a unity government. British officials said they saw calls for elections by Abbas as a way forward.
Abbas also said he would pursue in the meantime efforts to form a national unity government which could persuade Western countries to end sanctions imposed on the Hamas administration.
Blair said that the recent violence between Abbas's security forces and Hamas supporters showed that Palestinians urgently needed to form a government that Israel, Europe and the US would be ready to talk to.
"I think the most important thing is that on the Palestinian side, one way or another, we have a fully functioning authority with which the rest of us can deal," he said in Ankara.
"This is what I hope we will be able to agree during ... this visit," he said.
Blair's spokesman said before Abbas's speech that new elections could break the logjam between Palestinian factions.
Hamas rejected as a coup attempt the call for early elections, but Britain says Hamas, which won elections in January and has a parliamentary majority, should not control the agenda.