Erdogan was explaining all the problems with the USA presence in Iraq and Syria and was irritating Trump, according to a senior administration official who received a detailed readout of the phone call between both presidents.
Manbij was at the centre of an agreement the US and Turkey reached in June under which Kurdish forces were to withdraw.
Mattis, 68, had said he would leave at the end of February to allow a smooth transition for the next chief of the world's top military power - but a reportedly angry Trump accelerated his departure by two months.
Trump, for his part, has never been a fan of sending US troops out for battles overseas.
The problem is that Turkey also views Kurdish forces allied with both the U.S. and Israel as terrorists, and experts are convinced that the Turkish military will soon engage the Kurds.
Turkey was a rare ally that lauded Trump's momentous decision on Syria, a country where it will now have a freer rein to target US-allied Kurdish fighters who have played a major role in the war against IS but are deemed terrorists by Ankara.
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The town of Manbij has been one area of friction between the USA and Turkey, which has vowed to clear the area of the YPG.
While Mattis' resignation followed Trump's announcement that he would soon pull all of the approximately 2,000 us troops out of Syria, officials said that the decision was the result of an accumulation of disagreements.
Newsweek learned the troop withdrawal was made a week prior to Trump's Twitter announcement, in which the president informed military officials of his decision after a phone call with Turkish President Recep Tayyip Erdogan.
He said up to 15,000 Syrian fighters trained in Turkey are ready to take part in the operation.
Mr Hammoud said that fighters of the Syrian National Army are now waiting for orders from Turkish command and explained that a timeline for the offensive is contingent on agreements between Ankara and Washington.
The former North Atlantic Treaty Organisation commander went on to say, "What the United States had going for it is the reputation of reliability, consistency-that we were going to be there through thick and thin". But the extremists are largely confined to a remote desert enclave hundreds of miles (kilometres) to the southeast of Manbij.
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Maj. Richard Bates, the Marine contingent's officer in charge, said the only information they have on the troop drawdown has come from media reports.
American forces are still stationed in and around the town of Manbij.
With the U.S. army gone from Syria, it is expected that President Erdoğan will launch an offensive against the Kurdish autonomous region in Northern Syria, which it considers allies of the Kurdistan Workers' Party.
He referred to Turkey's cross-border offensive launched in August 2016 against the IS in northern Syria and said Ankara would take all measures to avoid a power vacuum after the United States withdrawal. "This will have more to do with the coordination of the withdrawal process in the field".
Meanwhile, Senate Majority Leader Mitch McConnell, R-Ky., joined leading Republicans on foreign affairs in urging Trump to reconsider his decision to withdraw American forces from Syria and called it "a premature and costly mistake".
Damascus has bolstered its forces in eastern Deir ez-Zor, around al-Mayadin and al-Bukamal, across the Euphrates River from territories where the Kurdish-led Syrian Democratic Forces (SDF) are battling ISIS, the Syrian Observatory for Human Rights reported.
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