In separate statements, France and Austria signalled they would also take tentative steps towards official contact with non-Hamas members of the government.
Israel, however, says it will continue to shun the government, which is made up of Fatah, Hamas and several other smaller factions.
Fayad, an independent, said his meeting with Walles was aimed at bringing to an end the economic boycott that has crippled the Palestinian territories and encouraged inter-faction fighting.
Micaela Schweitzer-Bluhm, spokeswoman for the US consulate, declined to confirm the meeting took place.
A spokeswoman for Javier Solana, the EU foreign policy chief, confirmed that the bloc's Middle East envoy, Marc Otte, had held talks on Tuesday in Gaza City with Ziad Abu Amr, the Palestinian foreign minister, an independent member of the cabinet.
"This is just a ploy to regain international hand-outs with smoke and mirrors"
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Mustafa Barghouti, the minister of information and unity government spokesman, told Al Jazeera that the government was abiding by international law.
The new government has been repeatedly asked to renounce violence, to recognise Israel and to abide by previous peace agreements.
"We are ready to have a complete ending to all violence through the establishment of complete, comprehensive and reciprocal ceasefire with Israel," Barghouti said.
"We don't need resistance if there is no occupation.
"We are the oppressed. We are the people who are occupied. If there should be conditions, they should be put on Israel."
Resistance is a word that could be key in securing full recognition for the new Palestinian government.
Condoleezza Rice, the US secretary of state, has said some forms of resistance are tantamount to "terrorism" and refuses to deal with the new Palestinian government or to lift economic sanctions.
Palestinian officials have repeatedly called for an end to the international aid boycott, as the Gaza Strip spiralled into economic chaos and violence.
But officials said on Tuesday that the EU was in no hurry.
One official in Brussels said on condition of anonymity that the EU needed "to see real action from the government, and that won't happen from one day to the next".
The EU is by far the biggest aid provider to the Palestinians. It donated $900m last year, without any of the money reaching the Hamas government.
Most of the funds went through a temporary mechanism set up to provide fuel for hospitals and generators and pay temporary allowances to those most in need, and officials expect that to evolve.
Cristina Gallach, Solana's spokeswoman, said: "We'll keep using the mechanism for a while. It allows us to give aid. We're not going to close the door but we're not going to open it right up either."
However, Jonas Gahr Stoere, Norway's foreign minister, said the Palestinian coalition was a "historic event" whose alternative would have been continued violence in the Gaza Strip and the West Bank.
Stoere told a news conference: "Norway will deal with members of the new Palestinian government as representatives of a broad and representative unity government."
| Raymond Johansen, Norway's deputy foreign|
minister, met Ismail Haniya on March 19 [EPA]
He said it was "essential that the unity government gains control of the security situation ... and that the rocket attacks on Israeli areas cease".
"We particularly call on Israel to take a constructive approach to the unity government, for example, by releasing withheld Palestinian revenues from taxes and fees and by increasing the freedom of movement for the Palestinian population," he said.
Norway's left-of-centre government has had warm relations with the Palestinians and avoided using the word sanctions or boycott after Hamas gained power, although it placed "restrictions" on aid and other political contacts.
"On the basis of the new government's political platform, Norway expects the Palestinian authorities to respect basic international standards as regards compliance with previously concluded agreements, renunciation of violence and recognition of Israel's right to exist," Stoere said.
Stoere praised efforts by Mahmoud Abbas, the Palestinian president, to form the new government as well as efforts by Washington in forging ahead with peace efforts.
"We will continue to support President Abbas actively in his efforts to establish an independent Palestinian state free of occupation," Stoere said.