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TOKYO, July 23 (Reuters) The dollar hit a record low against the euro on Monday, hurt by worries that problems in the U.S. subprime mortgage sector could harm consumers and slow U.S. growth.

The dollar also languished against the yen after falling to six-week lows versus the Japanese currency on Friday, when a fall in U.S. equities eroded investors' appetite for risk and prompted them to unwind some bets against the low-yielding currency.

''The key factor this week will be whether share prices will continue to fall and whether we will see more flight to quality,'' said a trader for a major Japanese bank.

The euro stood at $1.3836 as of 2346 GMT, hovering near a record high around $1.3845 struck in early Asian trading on Monday.

The dollar stood at 121.32 yen little changed from U.S. trading late last week. The dollar fell as low as 120.87 yen on electronic trading platform EBS on Friday, the lowest since early June.

The yen could rise further if equities markets fall and prompt more unwinding of risky yen carry trades, the Japanese bank trader said.

Carry trades involve the selling of low-yielding currencies such as the yen to invest in higher-yielding currencies and assets.

But market players are also keeping their eyes on possible flows from Japanese investment trusts targeting overseas assets that are to be launched later this week, the trader said.

Japanese households' search for higher yields abroad via investment trusts and leveraged currency margin trading have contributed to the yen's broad slide this year that has driven the currency to record lows against the euro and 16-year lows against the Australian dollar.

REUTERS DKS PM0627