His Middle East envoy Jason Greenblatt met Israeli and Palestinian leaders on Tuesday and White House senior adviser Jared Kushner was due in the region on Wednesday.
Kushner said Trump asked him to personally convey the condolences of the American people.
Discussions have been ongoing since that May 22 trip, the official said.
On Tuesday, US Secretary of State Rex Tillerson said the Palestinian Authority had agreed to halt payments to the families of slain attackers, including suicide bombers. In that period, some 251 Palestinians were killed by Israeli fire. The two arrived in the region amidst the White House's efforts to revive the long-stalled peace talks.
The settlers would live in the temporary accommodation while work continues on building more permanent homes, the spokesman added.
"Nabil Abu Rdainah, a spokesman for Palestinian President Mahmoud Abbas, called the ground-breaking "a grave escalation and an attempt to foil efforts by the American administration to revive negotiations", especially (before) the arrival of the USA envoys".
The expansion of existing settlements on the West Bank - territory which Israel occupied during a conflict in 1967, has been a major point of contention in the Israeli-Palestinian conflict.
Death toll rises to 3 in blast at Colombia mall
All vehicles entering the parking garage are screened by bomb-sniffing dogs and security guards are present throughout the mall. The rebel group the National Liberation Army , the second largest in the country after FARC, condemned the attack on Twitter .
"Incidents such as this underscore why it is vital to realize President Trump's vision of a Middle East free from threats of terrorism and extremism", the statement said.
"It's very hard for any party in the region to say no" to Trump, said Shapiro, now a visiting fellow at the Institute for National Security Studies in Tel Aviv.
Netanyahu has in the past given his conditional backing to two states.
While preliminary work has already begun, plans for the settlement have yet to go through the approval process, meaning actual construction work has yet to begin.
In 2010, a detailed report examining BBC News showed that the news agency often pitched its stories from a pro-Palestinian perspective, quoting organizations known to be critical of Israel.
All three Palestinians were said to have been from the West Bank village of Deir Abu Mashal and witnesses said their bodies stayed on the ground for hours. "Why buy the cow when you can get the milk for free?" It also reported that Israel had advanced plans for nearly 5,000 new settlement units so far this year - nearly twice those seen in all of 2016.
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