Trump says in a pair of tweets Friday evening that Craft "has done an outstanding job representing our Nation" and he has "no doubt that, under her leadership, our Country will be represented at the highest level."
The US Department of State spokesperson said she took the decision "in the best interests" of her family.
If confirmed by the Senate, she would succeed Nikki Haley, who said in October she would be leaving the UN post at the end of the year.
The world doesn't agree with the United States when it comes to putting pressure on Cuban economy.
Ambassador to the UN Nikki Haley will resign from her post by the end of the year. During her tenure she tirelessly defended the Trump administration in the face of criticism from both inside and outside the US.
Does the resignation of the US ambassador to the United Nations mean there might be a change in America's hostile attitude towards the UN?
US President Donald Trump says he has accepted the resignation of UN Ambassador Nikki Haley, who will be leaving at the end of the year.
The Ahvaz National Resistance has been in the headlines following the attack in Iran last week. The little-known separatist militant group has no international recognition; Iran accuses the US and Gulf States of backing it.
There are expectations the meeting will have a different tone from last year when wary world leaders weren't prepared for US president's brand of diplomacy or for his determination to push an "America first" agenda.
A full-scale regime assault on Syria's last opposition and rebel-held province of Idlib would sabotage the ongoing political process, Turkey's presidential spokesman Ibrahim Kalin said after a cabinet meeting chaired by President Erdogan.
"Fear" by the award-winning journalist who helped bring down former US president Richard Nixon has left aides and officials scrambling for cover as the book offers explosive insider anecdotes about the Trump administration.
As residents in Idlib look to Turkey for security, UN envoy for Syria urges Turkish President Erdogan and Russian President Putin to "make a telephone call, organise a formula" which could help avoid a battle ending in a bloodbath.
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