By Anna Irrera and Lawrence White

NEW YORK/LONDON, June 13 (Reuters) - Fast-growing British digital bank Monzo is launching in the United States through a limited rollout of its app-based checking account and connected debit card, it said on Thursday.

Monzo will make available a few thousand cards at in-person sign-up events over the next weeks in cities including Los Angeles, San Francisco and New York, as it seeks to replicate the word-of-mouth support that boosted its UK launch, it said.

It hopes to attract an engaged early-user base which will provide feedback to help tailor the company's offering to the U.S.

market, Chief Executive Tom Blomfield said in an interview.

"We are taking it slow to start with," Blomfield said. "We want to understand how U.S. consumers think and feel about their money."

Starting on Thursday, potential customers will also be able to join an online waiting list to receive a card, Monzo said.

Monzo, which was founded in 2015 and is valued at more than 1 billion pounds ($1.3 billion), is one of Europe's best-known "neobanks" that have launched in recent years to compete with established banks by offering more user-friendly digital services.

It has more than 625 million pounds ($793 million) in deposits from around 2 million customers, and says it adds 200,000 users per month.

The bank has seen rapid success in winning customers from the six large incumbent banks in Britain such as Lloyds and RBS, although many customers have yet to switch their monthly pay cheques to Monzo.

Around 30 percent of customers use Monzo as their primary bank account, Blomfield said.

In the United States, it will face competition from incumbent banks and their digital offshoots, as well as banking startups such as Chime and Varo Money, and other financial technology companies that have recently launched checking accounts.

It also faces a tougher regulatory landscape than at home.

"For UK fintechs looking to fly the nest, one major contrast will be the complexity of federal- and state-level laws, compared to the UK?s fintech-friendly regulatory environment," said Richard Lumb, group chief executive for financial services at consulting firm Accenture.

Monzo is launching in the United States with no minimum balance requirements and no monthly fees or foreign transaction fees, but will not pay interest on deposits.

The company has applied for a U.S.

banking licence, Blomfield said. It is launching in the country through a partnership with Ohio-based Sutton Bank, which is a member of the Federal Deposit Insurance Corporation.

($1 = 0.7879 pounds) (Reporting by Anna Irrera and Lawrence White; Additional reporting by Iain Withers; Editing by Sinead Cruise and Mark Potter)