Pompeo said on Friday that Washington recognised "the Turkish people's right and (Turkish President Recep Tayyip) Erdogan's right to defend their country from terrorists".
"Nothing has changed", one defense official told the Journal, adding: "We don't take orders from [National Security Adviser John] Bolton".
"Russia, Iran and Syria have been the biggest beneficiaries of the long term USA policy of destroying ISIS in Syria - natural enemies", Trump continued.
The U.S. -led coalition in Syria is beginning to withdraw troops from the country. Also, U.S. troops are among 200 to 300 coalition troops at a garrison in southern Syria known as al-Tanf, where they train and accompany local Syrian opposition forces on patrols to counter the IS group.
US Secretary of State Mike Pompeo earlier this month said that ensuring the Turkish military does not massacre the Kurds would be a key priority for the United States following the Pentagon's withdrawal of its troops from Syria.
Erdogan has said his military is prepared to attack swaths of Syria under the control of the Kurdish People's Protection Units.
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A spokesperson for the US -led coalition against the Islamic State militant group (ISIS) said the withdrawal had gone ahead despite mixed messages from the White House over the fate of the 2,000 troops operating in the country.
In Cairo on Thursday, Secretary of State Mike Pompeo said that although Trump has made a decision to bring troops home, he will keep up the fight against the IS group more broadly.
The United States has started the "deliberate withdrawal" process of its forces from Syria, US military officials confirmed on Friday, but they refused to provide any details on exactly what troops and equipment were being moved.
Turkey views the US-backed YPG Syrian Kurdish militia as an extension of the Kurdistan Workers' Party (PKK), which has waged a 34-year insurgency in Turkey for Kurdish political and cultural rights, mostly in southeastern areas near Syria.
"We will very soon mobilize to eliminate the terrorist organization in Syria", Erdogan said. US forces took a similar approach in neighbouring Iraq, starting in 2014, but in that case, they had a willing partner in the Iraqi government, whereas in Syria, the U.S.is present without the blessing of President Bashar Assad.
Pompeo stressed those fighting alongside the US are not terrorists and deserve protection. -Turkish consultations as part of the "deliberate and coordinated" withdrawal of American forces from Syria.
Initial indications from the White House were that USA forces would be withdrawn from Syria in 30 days.
America's operations against the Islamic State of Iraq and Syria (ISIS) in the country were to continue during the withdrawal process.
Media captionWas Trump right to say IS is beaten?