Esper had spoken about a number of topics related to Iran, but it was his comments on Iraq that raised Yingst's ire.
The letter claimed that coalition forces will leave Iraq and came a day after Iraqi lawmakers voted to expel the American military from the country.
Yingst then proceeded to point out how Esper's assessment of the situation in Iraq was incorrect.
Iraq's parliament and outgoing prime minister have called for the forced withdrawal of all western troops from the country.
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"In due deference to the sovereignty of the Republic of Iraq, and as requested by the Iraqi Parliament and the Prime Minister, CJTF-OIR will be repositioning forces over the course of the coming days and weeks to prepare for onward movement."
The NATO training mission in Iraq, established in 2018, is separated from the much larger foreign military deployment in the US-led country.
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General Jonathan Vance, chief of defense personnel, announced the "operational break, quot; in a letter posted on Twitter to the families of deployed military personnel".
America's military strategy in Iraq has been thrown into disarray after the Pentagon admitted a top U.S. general mistakenly informed the Iraqi government his troops were preparing to leave.
"These troops can be brought back at any time if the training in Iraq is to resume", a statement by the defence ministry said.
The Pentagon had said an unsigned draft version of the letter had been mistakenly sent, but the Iraqi premier disputed that claim. "The Iraqi government must work to end the presence of any foreign troops on Iraqi soil and prohibit them from using its land, airspace or water for any reason".
Vance did not reveal how many Canadian troops were being pulled out of Iraq, and the Department of National Defence later said it would not provide that information for security reasons. "It'll make Iranian sanctions look somewhat tame", Trump said Monday.
US officials say there is a repositioning of forces for purposes of force protection.
Foreign ministry spokesman Geng Shuang said in Beijing on Tuesday that the USA has an worldwide obligation to issue visas for such meetings as the host country of the United Nations.
Canada's military aid to Iraq stems from 2014 after Islamic State militants cut a swath of destruction across Syria and Iraq.