* Euro, AUD, NZD retreat from milestone peaks
* Investors wary of China's response to Houston consulate closure
* S. Korea deep in recession
* Graphic: World FX rates in 2020 https://tmsnrt.rs/2RBWI5E
By Tom Westbrook
SINGAPORE, July 23 (Reuters) - The dollar crept off milestone lows against other majors on Thursday, and held on to gains against the yuan, as heightened Sino-U.S. tensions kept currency markets cautious.
The United States gave China until Friday to close its consulate in Houston amid accusations of spying, and President Donald Trump said it was "always possible" other Chinese missions could be ordered to close as well. has vowed to respond, and the escalation in tension between the world's two largest economies sent the yuan CNH= on its sharpest slide in nearly two months on Wednesday and helped the greenback find support in Asia on Thursday.
The euro EUR=EBS sat at $1.1580, about 0.2% below a 21-month high of $1.1601, which it hit overnight in the wake of Europe's leaders agreeing on a coronavirus rescue package.
The Australian dollar AUD=D3 pulled back from a 15-month peak and drifted around $0.7151, while the kiwi NZD=D3 was a touch below Wednesday's six-month top at $0.6678.
Moves were slight and volumes were lightened by a public holiday in Japan.
"The market is still trying to ascertain whether this increase in geopolitical tension is going to be enough to derail the positive vibes we've been seeing," said Rodrigo Catril, senior FX strategist at National Australia Bank in Sydney.
"Recent history will tell you that the market will tend to digest this stuff and carry on in its merry way...but a bit of caution is warranted, and the yuan moving higher is probably the canary in the coalmine that we need to keep an eye on."
The yuan is a barometer of Sino-U.S. relations and it recovered a little from a one-week low, but kept to the weak side of the 7-per-dollar mark at 7.0030 in offshore trade.
DEAL WATCH
However, dollar gains were limited with the greenback barely lifting from a four-month low against a basket of currencies =USD , sitting at 94.931. July so far is its worst month against the euro since January 2018 and that weakness is fanning out across the board.
Caution and dollar softness helped the safe-haven Swiss franc CHF= to a four-month top of 0.9281 per dollar, but the yen JPY= was rangebound at 107.13 per dollar.
U.S.-China ties have worsened sharply this year over issues ranging from the coronavirus and telecoms-gear maker Huawei, to China's territorial claims in the South China Sea and clampdown on Hong Kong.
The U.S. State Department said the Chinese mission in Houston was being closed "to protect American intellectual property and Americans' private information."
Chinese state media said on Thursday that the move was a political ploy ahead of November presidential elections, and one source with knowledge of the matter told Reuters that China was considering closing the U.S. consulate in Wuhan in response.
Citi analysts expect some kind of Chinese reply, but they do not think it will derail the trade deal - which is the main focus for markets - and advise betting yuan rises.
"We think the Phase One trade deal is likely to hold into the U.S. election and the market may shift attention to China's relative economic outperformance," said Johanna Chua, a Citi strategist in Hong Kong, in a note.
Other threats to the global coronavirus recovery are also growing.
South Korea slipped into its first recession since 2003 as the country's exports fell by the most since 1963, showing Asia's fourth-largest economy has a considerable road back to recovery. day with more than 1,100 U.S. coronavirus fatalities also underscored the growing risk to recovery there. Weekly jobless claims due at 1230 GMT will offer the next checkup on economic progress.