Considered a terrorist group by the United States and the European Union, Hamas has taken steps in recent days that are seen as a bid to ease its international isolation while not alienating hardliners within the movement.
Before announcing Haniya as its new leader on Saturday, replacing Khaled Meshaal, who completed his maximum two terms, the movement that controls the Gaza Strip released a new policy document last week somewhat easing its stance on Israel.
The moves come with 82-year-old Palestinian president Abbas losing popularity and a behind-the-scenes succession battle taking shape.
Hamas remains deeply divided from Abbas's more moderate Fatah, which is based in the occupied West Bank.
Some analysts say the recent steps could eventually help smooth the way for Hamas's entry into the Palestine Liberation Organisation, which it has never joined, and open a path for dialogue internationally.
The PLO is considered the international representative of Palestinians both in the Palestinian territories and the diaspora.
Others warn however that Hamas still has much to do to significantly change the international community's attitude toward it, with many pointing out that it has not recognised Israel.
While its new policy document accepts the idea of a Palestinian state within territories occupied by Israel in the Six Day War of 1967, it continues to speak of liberating all of historic Palestine, including what is today Israel.
It stresses however that its struggle is not against Jews because of their religion but against Israel as an occupier.
In what is seen as a bid to improve relations with Egypt, the document also does not refer to the Muslim Brotherhood, which was closely linked to Hamas when the Palestinian organisation was formed.
"Ismail Haniya is the most appropriate person to promote this document to Arab and international leaders," said Gaza political scientist Mukhaimer Abu Saada.
The former Palestinian prime minister, he added, was from Hamas's pragmatic camp.
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One strategy could see Hamas seek to improve relations with European countries, a European official based in Jerusalem said, particularly with "Abbas under pressure at home and (US President Donald) Trump not giving any clear sign of willing to meet Abbas's basic demands".
In Washington last week, Abbas met Trump in their first face-to-face encounter, with the US president saying he wanted to achieve the decades-long goal of Israeli-Palestinian peace.
He has however pledged strong support for Israel and backed away from the United States' long commitment to a two-state solution, saying he could back one state if it meant peace.
- 'Unite the movement' -
The bitter split between Fatah and Hamas has taken a new turn in recent days.
Some analysts say it seems Abbas is seeking to increase financial pressure on Hamas in the impoverished Gaza Strip, but he risks being blamed for worsening conditions in the enclave of two million people.
"Hamas will intensify relations with those already talking to it and could possibly surprise all the critics and create huge embarrassment for Abbas," the official said on condition of anonymity.
Some diplomats have however said Hamas would need to do much more to convince Western countries to end its isolation, noting that the changes announced so far could be merely window-dressing.
Abu Saada said Haniya's attempts to improve relations with Arab states would be key.
But as the European official pointed out, he would have to "unite the movement behind him," in particular hardliners concerned with the recent moves.
Yahya Sinwar, a top commander in Hamas's armed wing, was named the movement's leader in the Gaza Strip in February.
Hamas late Sunday said in a statement Sinwar, Mussa Abu Marzuq and Ezzat al-Rishq had been elected to the movement's political bureau.
Hardliners yield influence in the strip, which has been under an Israeli blockade for 10 years.
Israel and Palestinian militants in Gaza have fought three wars since 2008.