* Dollar gains vs euro after Deutsche Bank shares hit record low
* Short-covering after U.S. debate boosts peso
* Relief after debate supports dollar (Updates prices, adds comments; changes byline, dateline, pvs LONDON)
By Sam Forgione
NEW YORK, Sept 27 (Reuters) - The U.S. dollar rose against the euro on Tuesday after concerns surrounding Deutsche Bank caused general unease over Europe's banking sector, while the Mexican peso rallied on short-covering after first U.S. presidential debate.
Deutsche Bank shares hit a record low on Tuesday before turning mostly flat a day after Germany's biggest lender said it had no need for German government help with a $14 billion U.S. demand to settle claims it missold mortgage-backed securities.
The euro was last down 0.51 percent at $1.1196, easing from an 11-day high of $1.1278 touched on Monday.
"Some of the concerns over the European banking system have caught fire or have come into focus more recently," said Mazen Issa, senior FX strategist at TD Securities in New York.
The perception among market participants that Democratic presidential candidate Hillary Clinton's performance in the first U.S. presidential debate was superior to that of Republican candidate Donald Trump boosted the peso.
The currency had touched a record low of 19.92 pesos against the dollar on Monday on concerns that a Trump victory would threaten Mexico's exports to the United States, its single biggest market.
The outcome of the debate led investors to cover peso short positions, said Richard Franulovich, senior currency strategist at Westpac Banking Corporation in New York.
Data from the U.S. Commodity Futures Trading Commission on Friday showed speculators had recently ramped up their bearish bets against the Mexican currency.
The dollar was last down 1.6 percent against the peso at 19.55 pesos after hitting an 11-day low of 19.44 pesos in early trading. The dollar was on track for its biggest daily drop against the peso in three weeks.
Relief that Clinton's performance was viewed as superior also likely helped the dollar gain against the euro given uncertainty surrounding a potential Trump presidency, Franulovich of Westpac said.
Markets have tended to see Clinton as the candidate of the status quo, while few are sure what a Trump presidency might mean for U.S. foreign policy, international trade deals or the domestic economy.
"You might argue that currencies like the yen and the euro had a defensive quality about them that were benefiting from Trump risk," he said.
The dollar was last mostly flat against the yen at 100.34 yen after falling 0.7 percent against the Japanese currency on Monday. The dollar index, which measures the greenback against a basket of six major currencies, was last up 0.33 percent at 95.609. (Reporting by Sam Forgione; Additional reporting by Anirban Nag in London; Editing by Meredith Mazzilli)