Netanyahu said he was to speak with the billionaire businessman turned president later in the day, while Israeli officials also approved hundreds of new settler homes that had been postponed until after Trump took office.
Beyond that, hardline Israeli ministers were pushing a plan to unilaterally annex a large Jewish settlement near Jerusalem in the occupied West Bank, a move many say could badly damage prospects for a two-state solution.
One minister was reportedly promoting his own plan to annex a number of other settlements in the Jerusalem area.
"This evening there will be a telephone conversation between President Trump and myself," Netanyahu said at the start of a cabinet meeting.
"There are many issues between us, including the Israeli-Palestinian issue, the situation in Syria and the Iranian threat."
Trump has pledged strong support for Israel and vowed during his campaign to recognise Jerusalem as the country's capital despite the city's contested status.
Israeli right-wing politicians have welcomed his election, with hardliners who oppose a Palestinian state hoping it will allow them to move forward with their long-held goal of annexing most of the West Bank.
Former president Barack Obama's administration repeatedly criticised Israeli settlement building and declined to veto a December 23 UN Security Council resolution condemning it.
Trump called for the resolution to be vetoed.
The United States is Israel's most important ally, providing it with more than $3 billion per year in defence aid.
'We can finally build'
In an initial move following Trump's inauguration, Israeli officials on Sunday approved building permits for 566 settler homes in annexed east Jerusalem.
"The rules of the game have changed with Donald Trump's arrival as president," Jerusalem Deputy Mayor Meir Turjeman told AFP.
"We no longer have our hands tied as in the time of Barack Obama. Now we can finally build."
A draft bill to annex the Maale Adumim settlement was also expected to be discussed by ministers on Sunday.
Netanyahu however was reportedly seeking to delay a vote on the measure by a panel of ministers, arguing Trump's team had indicated no unilateral moves should be taken so soon.
Annexing the settlement unilaterally would set off alarm bells globally, with many warning that it would be another step towards dividing the occupied West Bank between north and south, making a contiguous Palestinian state difficult to achieve.
But for some Israeli ministers, that is precisely the point. Key members of Netanyahu's coalition oppose a Palestinian state.
"We have to tell the American administration what we want and not wait for orders from the administration," Justice Minister Ayelet Shaked of the Jewish Home party told Israel's army radio on Sunday.
"There is no reason for us not to take unilateral steps that we believe are correct."
'Block east Jerusalem'
Maale Adumim, in a strategic location east of Jerusalem, includes some 37,000 residents.
Some previous peace proposals have envisioned Maale Adumim becoming part of Israel in land swaps agreed with the Palestinians, but not in a unilateral move.
It was unclear whether the proposal would also apply to another key area referred to as E1, located between the settlement and east Jerusalem.
The Palestinians see east Jerusalem as the capital of their future state, while Israel views the entire city as its capital.
Settlement watchdog Ir Amim said "the annexation of Maale Adumim and E1 will block east Jerusalem on its eastern side, swallow up its last development reserves and deepen the detachment from the West Bank.
"Given Maale Adumim's critical location in the heart of the West Bank, the international community has for years been following with special concern all developments in this area, seen as a touchstone for the viability of a two-state solution."
Israel occupied the West Bank and east Jerusalem in 1967. It later annexed east Jerusalem in a move never recognised by the international community.
Some 400,000 Israeli settlers live in the West Bank, with another 200,000 in east Jerusalem. In comparison, some 2.9 million Palestinians live in the West Bank and east Jerusalem.
Settlements are viewed as illegal under international law and major stumbling blocks to peace efforts as they are built on land the Palestinians see as part of their future state.
