As European Union foreign ministers approved a decision to suspend aid to the Palestinian Authority, Mr Abbas called on the international community to end its "unfair" treatment of his people and instead help them realise their dream of independence.
Mr Abbas will embark on a tour of Europe and North Africa this month in a bid to counter Israel's own diplomatic offensive, which has seen acting premier Ehud Olmert institute a boycott of any foreign officials who make contacts with Hamas ministers.
"We call on the Israeli government to stop these measures which are only intended to isolate the Palestinian Authority," Mr Abbas said in a speech at his West Bank headquarters in Ramallah.
"We will not accept this, we will not allow this to become a reality. We will emerge from this isolation whatever the cost."
Mr Olmert said on Sunday that all contacts would be frozen with what he called a "hostile authority", referring to Hamas's refusal to renounce violence and recognise Israel's right to exist.
"We say to the Israeli government that we are a peaceful nation but we want our rights," said Mr Abbas, whose own Fatah faction was defeated by Hamas in a January parliamentary election.
He said that the Palestinian people wanted what had already been promised to them, mainly a viable state.
"Is this too much to ask? Is this too much for the world to handle?" he said.
Palestinian prime minister Ismail Haniya has accused the EU and the US, which both regard Hamas as a terrorist organisation, of trying to "blackmail" his government by cutting funds to a democratically elected government.
Washington and Brussels, however, insist that the Islamists, who have held off attacks for the past year, must unequivocally renounce violence and recognise Israel if they want to be brought in from the cold.
Hundreds of Palestinian youths took part in a protest in Gaza City on Monday against the EU move, hurling eggs at the United Nations headquarters from where local EU staff are currently working.
But British Foreign Secretary Jack Straw defended the funding freeze.
"Hamas has got to recognise that being elected as a government, democratically, they have responsibilities as democrats to do what everybody else has to do as a democrats, which is to eschew violence," he said at the meeting in Luxembourg.
The precarious state of the Palestinian economy was underlined when finance minister Omar Abdelrazek told news agency AFP he had a US$120 million monthly budget shortfall despite receiving US$35 million from the Algerian government.
Algeria will be one of the stops on Mr Abbas's tour of North Africa and Europe that will also take him to France and Turkey.
Mr Abdelrazek also announced that Kuwait, Saudi Arabia and the United Arab Emirates had pledged US$80 million in aid.
"We have received pledges from the Arab world that will help us operate for several months," he said.
Making good on Mr Olmert's pledge to cut all contacts with the Hamas-led administration, Israel ordered the symbolic closure on Monday of a security liaison office in Jericho in the West Bank.
Mr Olmert has consistently said that he would have no contact with a Hamas-led government but the move to cut contacts at such a low-level indicates a new determination to make life as difficult as possible for Hamas to govern.
The acting premier has also ordered the Israeli army to continue its bombardments of northern Gaza in a bid to put a halt to cross-border rocket attacks.