Abbas also promoted the idea of a cabinet of technocrats as a way to ease crippling Western sanctions, but he pledged not to force it on Hamas, and the Islamic ruling party was cool to the idea.
Abbas addressed reporters for more than an hour at his headquarters in the West Bank city of Ram Allah on Tuesday evening.
He said talks on forming a unity coalition with Hamas were dead, due to its refusal to soften its stance towards Israel.
"In the near future we need to reach options that will allow us to get out of this crisis as soon as possible... It is impossible to remain in this situation."
He said the technocrat idea of a cabinet made up of professionals instead of politicians should be "considered seriously" as a way out of the current deadlock.
"[Hamas] say a government of professionals is an American option. What is this? They say ... this is a Zionist option, that they must stop this - these statements do not frighten us."
Hamas has said it believed a unity government was still possible, but it has ruled out recognising Israel.
The power struggle between Abbas's Fatah and Hamas has dashed the hopes of Palestinians that Western sanctions will be lifted.
There has been fierce fighting this month between fighters from Hamas and Fatah in which 18 people were killed, sparking fears of civil war.
Abbas did not say what his options were, but his aides said he might call fresh elections, appoint an emergency government or hold a referendum to let the Palestinian people decide.
Asked if he would call a referendum, Abbas said: "If there is no constitutional text on an issue I seek, I will go to the people and hold a referendum on that issue."
While the Palestinian basic law, which serves as a constitution, allows the president to sack the government, it does not mention other alternatives such as calling early polls.
"If I cannot solve the people's problems, I am worthless"
Hamas has accused Fatah of trying to topple the government. It warned of more fighting if Abbas carries out his threats.
Hamas defeated Fatah in parliamentary elections in January, prompting the West to cut off crucial official aid over the group's refusal to recognise Israel and renounce violence.
"A government that is incapable of lifting the siege is worthless," said Abbas, referring to the Western embargo and Israeli restrictions on freedom of movement and goods.
"If I cannot solve the people's problems, I am worthless."
Abbas said efforts to arrange a summit with Ehud Olmert, the Israeli prime minister, were being hindered by the issue of Palestinian prisoners.
Olmert had been expected to free a large number of prisoners held in Israeli jails as a gesture to Abbas, but that was put on hold when Palestinian fighters captured an Israeli soldier, Gilad Shalit, in a cross-border raid from Gaza in June.
"Everything has stopped because Israel is linking the release of prisoners to the release of Shalit," Abbas said.
In a separate development, Jack Wallace, the US general-consul in Jerusalem, has denied reports of a $42 million transfer from the US administration to Fatah, Aljazeera reports.
Following a meeting with Abbas, Wallace said the US administration would not offer financial assistance to political parties, insisting the media claims to this effect were baseless.