* Ukraine to ease fixed currency rate from Tuesday

* Battered economy shows smalls signs of recovery

KYIV, Oct 2 (Reuters) - Ukraine's central bank said it would bring in a more flexible exchange rate from Tuesday, relaxing the official peg it has had throughout the war with Russia in a move to boost the economy.

Central Bank Governor Andriy Pyshnyi said financial stability in Ukraine had climbed to a "historic maximum," allowing the central bank to start easing wartime restrictions in a bid to help the economy and businesses.

"Compared with July last year, the situation is radically different," Pyshnyi told an online media briefing.

"This will and should make us significantly stronger."

When Russia invaded in February 2022, the central bank immediately imposed restrictions and pegged the hryvnia currency at an official rate of about 29 to the U.S. dollar. By July 2022 it was forced to devalue the currency to 36.57 to the dollar.

But over the last several months the economy has shown signs of recovery, with inflation slowing and business sentiment improving.

The central bank said it would shift to a "managed flexible" exchange rate and was ready to intervene in the foreign exchange market as needed to avoid excessive volatility.

The National Bank of Ukraine said in a statement that the exchange rate would be determined by interbank foreign exchange operations with the "active participation" of the central bank.

Timothy Ash, senior strategist at BlueBay Asset Management, said unfreezing the exchange rate was a "sign of confidence in the durability of the economy through the war, strong Western financial backing, and the understanding that having a competitive exchange rate will be important in terms of successful recovery and reconstruction."

Serhiy Nikolaichuk, a deputy central bank governor, said the hard currency deficit stood at under $3 billion a month, due to seasonal factors, up from about $2 billion in the summer.

Central bank officials said they planned to continue to ease restrictions further as circumstances and the economic situation allow.

The central bank said in a statement that the new exchange rate would "strengthen the stability of the Ukrainian economy and the foreign exchange market, promote their better adaptation to changes in internal and external conditions, and reduce the risks of accumulating currency imbalances that can be generated by long-term maintenance of a fixed exchange rate."

It would also be "an important prerequisite for a return to inflation targeting in the future," it said, adding that maintaining exchange rate stability would remain a priority task for the NBU.

Ukraine's central bank hard currency reserves stood at over $40 billion at the start of September. (Additional reporting by Yuliia Dysa; Editing by Tom Balmforth and Alison Williams)