After their withdrawal, Turkey's military operation would be "completely stopped," Pence said.
"Great news from Turkey," President Trump wrote just before Pence's announcement on Twitter. "Millions of lives are saved!" He added.
Pence's whirlwind journey to Turkey took place just a week after the start of a military operation that had accelerated the withdrawal of US troops and the clutter of alliances in Syria's volatile civil war. Turkey's western allies have warned Erdogan that the fighting could lead to the revival of the militant group of the Islamic State.
The Trump administration was criticized for giving up its own allies: the Syrian Kurdish militia, who had teamed with the US military to fight the Islamic State. Turkey regards the Kurdish fighters as a serious threat because of their ties to the fighters in Turkey.
Pence said the Kurdish fighters would comply with the agreement reached between the US and Turkey. "We have repeatedly assured them that they will go out," he said, referring to the Syrian-Kurdish fighters.
Pence's mission came a day after the White House published a letter that Trump sent to Erdogan on October 9. I urge you to negotiate an agreement with the Syrian-Kurdish militias targeted by the Ankara military operation close.
"You do not want to be responsible for slaughtering people," Trump wrote, concluding, "Do not be a tough guy, do not be a fool!" The letter was written on the day the Turkish military operation began. Turkish officials told the BBC and other news agencies Thursday that Erdogan had thrown the letter in the bin.
"But the clearest answer to the letter written on October 9 was the Peace Spring operation," CNN Turk said, citing diplomatic sources and using the Turkish codename for its offensive.
Erdogan had repeatedly rejected appeals for a ceasefire and blamed Western allies for proposing to negotiate with "terrorists" as he referred to the Syrian-Kurdish militias associated with the Kurdish Workers' Party (PKK) fought for decades an uprising in Turkey.
Erdogan said Wednesday that "Turkey will never declare a ceasefire" and pledged plans to enforce a buffer zone to a depth of 20 miles on Syrian territory. The territory would stretch more than 280 miles from the northern city of Manbij to the Syrian border with Iraq.
Trump was criticized, among others, by his own Republican allies, who reported a hasty withdrawal of US troops.
On Wednesday, the US military withdrew from Raqqa, the former capital of the Islamic State, as well as Tabqa and a Lafarge cement plant headquarters in Jalabiya, Colonel Myles B. Caggins III, a US military spokesman. said in a tweet .
In the Cement Factory, US forces deployed F-15 jets after American troops left to carry out air strikes on parts of HQ to "destroy an ammunition cache and reduce the military usefulness of the facility," Caggins wrote.
In addition to ammunition, the strikes targeted a small area surrounded by blasting walls and housing and diesel generators, a US military official said about the state of anonymity over the sensitivity of the operation.
Lamothe reported from Washington.