"We are ready to begin negotiations on the basis of the roadmap from the minute the Israeli government is formed," Abbas said.
"There is no other way but direct negotiations based on international legitimacy."
Israel announced on Sunday it was severing all ties with the Hamas-led Palestinian government, regarding it as a "hostile entity".
The Israeli government has said it would maintain contacts with Abbas, though it ruled out full peace talks with him.
The United Nations has also advised its aid agencies to avoid meeting Hamas political leaders, including cabinet ministers, and to restrict contact to government officials.
"Contacts will continue at levels to ensure the continuation of humanitarian programmes," a senior UN official said on Tuesday.
In Moscow, the Russian foreign minister criticised the Western "boycott" of the Hamas government.
"Hamas must fulfil the demands made by international mediators .... but to have that happen, it's necessary to work with Hamas, not boycott it," Sergei Lavrov said.
"The rejection of aid to the Palestinians only because they chose a government made up entirely of Hamas members in the elections is wrong."
The EU, US and Canada all recently announced that they would suspend aid to the Palestinian government until Hamas renounces violence and agrees to recognise the state of Israel.
The EU says it will continue to provide assistance to the Palestinian people via humanitarian aid agencies.
Lavrov said: "It's necessary to find ways that would make it possible to provide assistance in a transparent and verifiable way for the goals of life-support. Russia plans to provide such assistance in this form."
Russia received a senior delegation from Hamas last month, the first country to do so after its election victory.