Trump described the truce as a “major breakthrough” negotiated by a team led by Vice President Mike Pence.
Syrian and Russian forces will deploy in northeast Syria to remove Kurdish YPG fighters.
Esper is likely to meet King Salman and Crown Prince Mohammed bin Salman.
India and Pakistan have a long history of bitter relations over Kashmir.
Erdogan agreed on Thursday in talks with US Vice President Mike Pence a five-day pause.
Turkey’s offensive created a new humanitarian crisis in Syria with 200,000 civilians taking flight, according to Red Cross estimates.
Pence had flown to Turkey to call for a halt in Turkey’s cross-border military operation.
Trump had the letter released to bolster his view that he did not give Turkey a green light to invade Syria.
Turkey pressed ahead with its offensive against the Syrian Kurdish YPG militia in northern Syria on Tuesday.
Trump’s Vice President also said he would travel to the region soon to try to mediate the crisis.
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