The planned new homes approved by Prime Minister Benjamin Netanyahu and Defence Minister Avigdor Lieberman may be the largest number to have been given the green light since 2013, said settlement watchdog Peace Now.
Settlements in both the West Bank and east Jerusalem are viewed as illegal under international law and major stumbling blocks to peace as they are built on land the Palestinians want for their own state.
The defence ministry announced the plans, saying most of the homes would be located within large settlement blocks in the West Bank.
Around 100 are to be located in the settlement of Beit El near Ramallah, it said.
Trump, his nominee for ambassador to Israel, David Friedman, and the parents of his son-in-law, Jared Kushner, have all reportedly contributed financially to Beit El.
According to Israeli newspaper Haaretz, Friedman has been president of a group called American Friends of Beit El Institutions.
It said the group raises about $2 million a year for Beit El.
Netanyahu referred to the settlement approvals on Twitter.
"We are building and we will continue building," he wrote.
The announcement comes after Israeli officials on Sunday approved building permits for 566 settler homes in annexed east Jerusalem.
'Encouragement' by Trump
The United Nations denounced the move, stressing "unilateral actions" were an obstacle to peace.
"For the secretary general there is no plan B for the two states solution," UN chief Antonio Guterres's spokesman Stephane Dujarric said.
Palestine Liberation Organisation secretary general Saeb Erekat said "the international community must hold Israel accountable immediately" over the expansion of settlements.
The Israeli leadership had been emboldened by "what they consider encouragement by American President Donald Trump", he told AFP.
Trump has signalled strong support for Israel, and Israeli right-wing politicians have sought to take advantage, with hardliners calling for an end to the idea of a Palestinian state.
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Netanyahu has said he still supports a two-state solution, but reportedly told ministers Sunday that all restrictions on building settlements in east Jerusalem were being lifted.
He also said Sunday he plans to expand construction in large settlement blocks in the West Bank, Israeli media reported, and that he foresees eventually bringing all settlements under Israeli sovereignty.
On Monday, in a reference to former US president Barack Obama, Netanyahu said "after eight years of withstanding huge pressures on a large array of topics, first and foremost Iran and the settlements, I definitely welcome the change of attitude".
"We're (now) facing great and significant opportunities for the security and future of the state of Israel."
Netanyahu and Trump spoke by phone on Sunday and the two leaders are to meet in early February.
Obama's administration grew frustrated with Israeli settlement building, warning it was eating away at prospects of a two-state solution.
The United States, in a rare move, declined to veto a December 23 UN Security Council resolution condemning Israeli settlement building, allowing it to pass 14-0.
Trump had called for the resolution to be vetoed.
Push from the right
Israel seized the West Bank and east Jerusalem in 1967. It later annexed east Jerusalem in a move never recognised by the international community.
The Palestinians see east Jerusalem as the capital of their future state, while Israel views the entire city as its capital.
Some 400,000 Israeli settlers now live in the West Bank, with another 200,000 in east Jerusalem.
In comparison, about 2.9 million Palestinians live in the West Bank and east Jerusalem.
Netanyahu currently heads what is seen as the most right-wing government in Israeli history and faces strong pressure from the settlement movement to expand construction.
On Monday, he spoke of the advantages the Trump presidency could provide, but also called for restraint.
Education Minister Naftali Bennett of the hardline Jewish Home party has been among those pushing for immediate moves, such as the unilateral annexation of a large West Bank settlement near Jerusalem called Maale Adumim.
Trump also vowed during his campaign to recognise Jerusalem as Israel's capital and move the US embassy to the city from Tel Aviv.
The move would constitute a break with decades of precedent and be in opposition to nearly all of the international community.
The White House has however since seemed to downplay the promise, saying it was only at the beginning stages of discussing such a move.