Hamas seized the Gaza Strip in 2007 in fighting with Fatah forces loyal to President Mahmoud Abbas and has ruled the impoverished desert enclave of two million people since then.
The cabinet session was the first in Gaza since 2014, Hamdallah told his ministers, and a major step in a reconciliation process promoted by neighbouring Egypt and other U.S.-allied Arab countries.
"Today, we stand before an important, historical moment as we begin to get over our wounds, put our differences aside and place the higher national interest above all else," Hamdallah said.
Israeli Prime Minister Benjamin Netanyahu, meeting legislators from his right-wing Likud party, said the Palestinians were engaging in "fictitious reconciliations" and he referred to Iranian funding for Hamas, which has fought three wars with Israel since 2008.
"The way we see it is very simple: Recognise the State of Israel, dismantle the Hamas military wing, cut the ties to Iran, which calls for our destruction," he said in remarks broadcast on Army Radio.
Hamas, considered a terrorist group by Israel and the West, last month disbanded its Gaza shadow government after Egypt, Saudi Arabia and the United Arab Emirates clamped an economic boycott on its main donor, Qatar.
But while Hamas handed over administrative responsibilities to a unity government originally formed three years ago, its armed wing remains the dominant force in Gaza.
A first sign of discontent was quickly evident in the new reconciliation drive: Hamas criticised Abbas's decision to await the outcome of talks Fatah plans to hold with the group in the next two weeks before lifting sanctions he has imposed on Gaza.
"ONE REGIME, ONE LAW"
"The government has assumed its responsibilities in Gaza and therefore, delay is not justified," Hamas spokesman Fawzi Barhoum said.
Abbas halted payments for Israeli-supplied electricity to the enclave in June, a step that has led to long daily blackouts, and he also cut salaries for Gaza civil servants.
Abbas told Egyptian TV station CBC on Monday there could be only "one state, one regime, one law and one weapon" in the Gaza Strip, reiterating a long-held position that security should be in the hands of only the Palestinian Authority (PA), which he heads, and that the PA must control border crossing points.
Both Israel and Egypt - whose intelligence chief arrived in Gaza to meet Hamas leaders, Hamdallah and officials from other Palestinian factions - maintain a partial blockade of Gaza, citing security concerns.
Israeli-Palestinian talks have been frozen since 2014 over issues such as Fatah-Hamas reconciliation and Israeli settlement-building in occupied territory.
Visiting the Jewish settlement of Maale Adumim in the occupied West Bank on Tuesday, Netanyahu said "thousands of housing units" would be added to the community of 40,000 people near Jerusalem. He gave no timeframe.
Israel has built about 120 settlements in the West Bank. About 350,000 settlers live there and a further 200,000 in East Jerusalem, among about 2.6 million Palestinians.
Most countries consider the settlements illegal and an obstacle to peace as they reduce and fragment the territory Palestinians need for a viable state. Israel disagrees, citing biblical, historical and political connections to the land and security interests.
(Writing by Jeffrey Heller; editing by Andrew Roche)
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)