The late Tuesday announcement came as security forces were preparing to evict the hardline occupants of a wildcat settlement outpost in line with a High Court ruling that determined the homes were built on private Palestinian land.
The planned eviction has been deeply unpopular with hardliners within the government, widely regarded as Israel's most right-wing ever, and the new building plans were widely seen as a sop to their supporters.
Dozens of security personnel were seen approaching the Amona outpost, northeast of Ramallah, headquarters of the Palestinian Authority, early on Wednesday in readiness to move out its residents.
Hundreds of hardline sympathisers, who had slipped past army roadblocks on foot, lit tyres around the outpost, an AFP correspondent reported.
Some threw stones at the media as residents started packing their belongings.
The former US administration of Barack Obama despaired of Israel's accelerating settlement expansion and, in a sharp break with longstanding policy, withheld its veto on a critical UN Security Council resolution in its final days.
But since Trump took office with top aides sympathetic to the settlement enterprise, the government has announced a string of new projects that will add more than 6,000 homes for Jewish settlers.
"Defence Minister Avigdor Lieberman and Prime Minister Benjamin Netanyahu have decided to authorise the construction of 3,000 new housing units," the defence ministry said in a statement.
According to the statement, 2,000 of the units are ready to be put on the market, while the rest are in various stages of planning.
"We're in a new era where life in Judaea and Samaria (the West Bank) is returning to its natural course," said Lieberman, who himself has long lived in a West Bank settlement.
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Since the January 20 inauguration of Trump, Israel has approved the construction of 566 housing units in three settlement neighbourhoods of annexed east Jerusalem and 5,502 more elsewhere in the West Bank.
On Thursday last week, Israeli officials gave final approval for 153 settler homes in east Jerusalem.
They had been frozen under pressure from the Obama administration, which had warned that settlements could derail hopes of a negotiated two-state solution.
Far-right lawmaker Moti Yogev, whose Jewish Home party is part of Israel's governing coalition, was quite open about the trade-off between the Amona eviction and the new settler homes.
Speaking to AFP at the outpost where he had joined residents in a show of solidarity, Yogev said that while evacuating Amona was "a bad decision" which he opposed -- "We will go."
"Yes, Amona will be destroyed, but against Amona we are going to build 3,000 new homes."
Trump has pledged strong support for Israel, and Netanyahu's government has moved quickly to take advantage.
"We are building and we will continue building," Netanyahu said last week.
The prime minister has said he sees the Trump presidency as offering "significant opportunities" after facing "huge pressures" from Obama.
The accelerated settlement expansion has deeply concerned those seeking to salvage a two-state solution to the Israeli-Palestinian conflict.
The international community considers all Jewish settlements on occupied Palestinian land as illegal and regards their construction as the biggest obstacle to a peaceful settlement of the conflict.
But in a significant break with the Obama administration, Trump's White House has not condemned any of the four settlement expansions announced by Israel since he took office.