The US and the EU are to normalise ties with the new Palestinian government, lifting embargoes on aid to support an administration without Hamas.US Secretary of State Condoleezza Rice promised “full assistance” to the Palestinian Authority and emergency humanitarian aid to Gaza via the UN.
The EU is assessing ways of resuming direct aid, while Israel said the new cabinet was a “genuine partner”.
Mr Abbas sacked the previous government after Hamas seized control of Gaza.
In a separate development on Monday, one Palestinian was killed and several injured after Palestinian gunmen and Israeli soldiers exchanged fire at the Erez crossing, the Israeli rescue service and Palestinian medics said.
The crossing is the main point for people travelling between Israel and Gaza.
Speaking in Washington, Ms Rice congratulated Mr Abbas’ choice as Palestinian Prime Minister, Salam Fayyad.
As a result of his appointment, she said, the US would resume diplomatic contacts with the Palestinians, suspended since Hamas came to power after winning elections in January 2006.
She criticised Hamas, which she said had tried to impose an extremist agenda on the Palestinian people.
“It is the duty of the international community to support those Palestinians who wish to build a better life, and a future of peace,” Ms Rice added.
She also announced $40 million (Â£20 million) of emergency aid to the UN Relief and Works Agency (Unrwa), which runs relief efforts in Gaza, now controlled by Hamas.
Earlier, in a 15-minute phone call with President George W Bush, Mr Abbas said the time was now right to push for new peace talks.
Israeli Prime Minister Ehud Olmert, who is to meet Mr Bush in Washington on Tuesday, said he considered the new Palestinian government a “genuine partner”.
And speaking at an EU meeting in Luxembourg, Israeli Foreign Minister Tzipi Livni confirmed that up to $800m (Â£400m) of frozen tax revenues held by Israel would now be transferred to the Palestinian Authority.
The EU and US imposed an aid embargo on the previous government after Hamas came to power.
After talks in Luxembourg, EU foreign ministers said the bloc would “resume normal relations with the Palestinian Authority immediately”.
The EU “will develop the conditions for urgent practical and financial assistance including direct financial support to the government”, the ministers said – as well as undertaking “intensive efforts to build the institutions of the future Palestinian state”.
The EU, the biggest donor to the Palestinians, continued to give emergency humanitarian aid during the ban on contact with the former Hamas-led government.
There are already concerns that Gaza’s 1.3 million residents could face shortages of food and other essential supplies in coming weeks because of an Israeli blockade of routes into and out of the territory.
However, an Israeli government spokesman denied that Israel aimed to make the humanitarian situation in Gaza any worse.
An Israeli fuel company, Dor Alon, also said it had restored normal fuel supplies to the Gaza Strip after Palestinians protested against an earlier suspension.