Gilad Erdan, a close ally of Prime Minister Benjamin Netanyahu, answered a motion in parliament by opposition lawmakers marking the massacre's anniversary.
"I think it is definitely fitting that the Israeli government formally recognise the Holocaust perpetrated against the Armenian people," Erdan, Israel's environmental affairs minister said.
Israel has long avoided acknowledging the mass killings of Armenians as genocide, in deference to already strained ties with Turkey which rejects that view.
Relations with Turkey have been tense since the 2010 killings of nine Turkish activists in a commando raid on a Gaza-bound ship. Turkey withdrew its ambassador to Israel after that incident and suspended military cooperation.
Erdan said the Israeli government had not formally changed its policy on the Armenian's past tragedy, adding: "we should definitely support holding an open and in depth discussion that analyses the data and facts."
Armenia, backed by many historians and parliaments, says about 1.5 million Christian Armenians were killed in what is now eastern Turkey during World War One in a deliberate policy of genocide ordered by the Ottoman government.
Successive Turkish governments and most Turks feel the charge of genocide is an insult. Ankara argues that there was heavy loss of life on both sides during fighting in the area.
Israeli lawmakers voted that the issue would face further debate in the education committee. Any parliamentary decision on the issue would not be binding on the government.
Yigal Palmor, a spokesman at Israel's Foreign Ministry, said Israel's formal position on the Armenian tragedy remained that the issue "must be decided by historians and not be subject to political deliberation."
The Armenian issue has stirred emotions in Israel where many feel that the Jewish people who suffered six million dead in the Nazi Holocaust during World War Two have a moral obligation to identify more closely with the Armenians' ordeals.
"Those who demand recognition of the murder are not engaged in lobbying but are simply seeking historic justice," Israeli Parliament speaker Reuven Rivlin, a member of Netanyahu's right-wing Likud party, said.
Nino Abesadze, a lawmaker with the centrist Kadima party, counseled against linking the issue to relations with Turkey.
"We must not link our sentiments about the Armenian tragedy to considerations about other dangers in the region. Events such as genocide are above politics," Abesadze said.