The Quartet - formed of the US, the European Union, Russia and the UN - cut off funding to the Palestinian Authority after Hamas came to power last year.
The unity agreement that Hamas signed with the long-dominant Fatah faction in Saudi Arabia last Thursday made no explicit commitment to recognise Israel.
A letter from Mahmoud Abbas, the Palestinian president, reappointing Haniya as prime minister, contained a call to the Hamas movement to "abide by the interests of the Palestinian people" and "respect" past agreements and international law.
"If the new government insists on the same stance, Abu Mazen [Abbas] would be moving from the positions that he had earlier"
Ehud Olmert, Israeli Prime Minister
Describing the Mecca deal as "historic", Haniya said: "In a meeting soon with president [Abbas], when he visits Gaza, we will resume the dialogue to conclude all the remaining issues so we can finalise details of a unity government."
He said Hamas would hold nine cabinet posts, with six going to Fatah. An independent candidate would become interior minister, a position that oversees security services.
Haniya said the unity agreement reflected a desire by Hamas and Fatah to end factional warfare that killed more than 90 Palestinians between late December and early February.
In Jerusalem, Israeli officials said earlier that Israel was considering suspending contacts with Abbas if the unity government did not meet international demands.
Condoleezza Rice, the US secretary of state, plans to hold a three-way summit with Abbas and Ehud Olmert, the Israeli prime minister, in Jerusalem on February 19.
"Palestinians must focus on the end objective and not get sidetracked by destructive actions"
Olmert told Israeli ministers that he needed to assess where Abbas stood after his power-sharing deal with the governing Hamas movement.
"Now they are one and they are one government ... If the new government insists on the same stance, Abu Mazen [Abbas] would be moving from the positions that he had earlier," a spokesman for Olmert said.
Israeli officials said any decision on whether to suspend contacts with the unity government would not be made until it is in place, a process that could take a month or longer.
Israel's response also depended on whether Abbas and the new government secured the release of captured Israeli soldier Gilad Shalit.
"Gilad Shalit can serve as a test," Olmert said.