Mr. Trump has called for curbs in settlement construction as part of an ambitious push to revive long-stalled peace talks to end the Israeli-Palestinian conflict.
In an interview published in February in the Hebrew edition of Israel Hayom, a newspaper considered supportive of Prime Minister Benjamin Netanyahu of Israel, Mr. Trump said he wanted Israel “to act reasonably,” after a series of Israeli moves to approve thousands of housing units for new settlers.
“There is limited remaining territory,” Mr. Trump added. “Every time you take land for a settlement, less territory remains.”
Days later, during a meeting between the two leaders at the White House, Mr. Trump made a public request to hold off on settlements.
Jerusalem and Washington have negotiated for weeks to try to reach an understanding on slowing or curbing settlement construction — by all accounts, without coming to a formal agreement.
During the Obama administration, Israel’s settlement activity was the source of constant friction. Secretary of State John Kerry in December harshly rebuked Israel while vigorously defending a United States decision to abstain from a United Nations vote condemning Israel on the settlements in the West Bank and East Jerusalem.
But Israel’s latest policy announcement was likely to have been coordinated with the White House, and the approval of the new settlement drew no strong condemnations from Washington.
Instead, there was an apparent understanding that Mr. Netanyahu should be allowed to fulfill his promise to compensate 40 families evicted from an illegal hilltop outpost by building them a new community.
Mr. Netanyahu has been walking a fine line between the new Trump administration, with which he wants to remain on good terms, and the right wing of his governing coalition, which has been pressuring him to increase construction and, in particular, to reject any freeze on building in certain areas.
The right-wing ministers were silent on Friday. The Yesha Council, the umbrella body representing the roughly 400,000 Jewish settlers in the West Bank, expressed cautious optimism but, reflecting the ambiguity of the new policy, said it would be monitoring the Israeli government closely to see if new building plans came to fruition.
Most of the world considers Israeli settlement activity in the territories captured from Jordan in 1967 to be a violation of international law. Israel considers the territories disputed and says the fate of the settlements must be decided in peace talks.
Most informal peace plans have envisaged border adjustments that would allow Israel to retain some of the major settlement blocs, especially those close to the 1967 boundaries, under any permanent agreement with the Palestinians, in return for land swaps.
The new policy announced on Friday made no explicit distinction between the blocs and the outlying settlements, in deference to the settlement advocates. It said that Israel would continue construction, where possible, within already developed areas of the settlements, and where that was not possible, would build adjacent to the last line of construction.
In cases where legal, security or topographical constraints made those scenarios impossible, new construction would be kept as close as possible to the existing built-up areas.
The boundaries of jurisdiction of some of the settlements are expansive, extending well beyond the built-up areas. The new policy seems aimed at preventing the construction of new neighborhoods far away from existing buildings, long a settler tactic aimed at controlling larger swaths of West Bank land.
But the new Israeli formula left the government much room for maneuver. While it might limit the territorial expansion of the settlements, it could also encourage an increase in the settler population by, for example, filling in available spaces with high-rise construction and by building more homes closer to existing amenities.
“When you build neighborhoods adjacent to the built-up area it encourages people to come,” said Shaul Arieli, an Israeli expert on political geography who prepared maps for past negotiations with the Palestinians and supports a two-state solution. “They become part of the settlement and have access to its services.”
More settlers outside the settlement blocs would clearly make any eventual Israeli evacuation more difficult. But Mr. Arieli said that for supporters of the two-state solution there were also advantages in the new policy, especially if new construction was mostly concentrated within the blocs, making them denser rather than spreading over a larger geographical area.
“The question,” he said, “is where they will build.”
