By Tom Arnold and Saeed Azhar

DUBAI, July 20 (Reuters) - Qatari banks may need more cash injections from the state and new sources of funding from outside the Gulf region because of the risk of more withdrawals by banks and investors from the Saudi-led group that is locked in a bitter dispute with Qatar.

Banks have been feeling the fallout of the feud with Saudi Arabia, the United Arab Emirates, Bahrain and Egypt, which cut diplomatic and transport ties with Qatar on June 5 and imposed economic sanctions.

They accuse Qatar of financing Islamist militant groups and allying with their regional adversary Iran - allegations Qatar denies.

The move prompted banks from the four Arab states to stem new business with Qatar and several Qatar banks have seen an outflow of deposits.

Total deposits at Qatar's five biggest banks rose by around 16.8 billion riyals ($4.6 billion) in the second quarter from the previous quarter, data released by the banks this week showed, as the state-owned Qatar Investment Authority stepped in with fresh funds.

But these injections have not allayed liquidity concerns for Qatari banks in the months ahead because of their high dependence on external sources of funding, rating agencies and analysts said.

"The immediate challenge that banks face is a liquidity challenge," Mohamed Damak, a senior director at Standard & Poor's, told Reuters. "If sanctions last for a longer period of time, investors' nervousness might be on the rise and banks can experience significant outflows of external funds."

Fitch Ratings estimates that the majority of deposits in Qatar from other Gulf Cooperation Council (GCC) countries are Saudi and United Arab Emirates' deposits, and that they are being withdrawn as they mature, said Redmond Ramsdale, senior director in Fitch's banks' team.

"Asian depositors so far appear to have rolled over, albeit at a slightly higher price," he said.

Less than $6 billion left Qatar over the last month, Qatar central bank governor Sheikh Abdullah bin Saud al-Thani said on July 10. Qatar banking deposits were 762.2 billion riyals at the end of May, according to central bank data.

Qatar Islamic Bank , Masraf Al Rayan and Al Khalij Commercial Bank saw a total outflow of 10.4 billion riyals between the first and second quarters.

Of the banks that have reported second quarter results so far, QNB, Commercial Bank of Qatar (CBQ), Doha Bank and Ahli Bank all experienced a rise in deposits during the second quarter.

Arqaam Capital analysts said that the Qatari government's decision to channel deposits to the banks was primarily driven by the banks' external vulnerability.

QNB, CBQ and QIB should have received deposits from the public sector since June as they derived 57 percent, 50 percent and 30 percent of their total funding needs from outside Qatar, they wrote in a research note.

Qatar banks have historically been heavily reliant on the government and state-related firms for deposits.

But a fall in oil prices since 2014 and the subsequent withdrawal of some government deposits from the banking system prompted some, including Qatar National Bank , the Middle East and Africa's largest lender, increasingly to secure liquidity from outside the region.

Of the 25 percent non-domestic banking deposits, more than half were from the GCC countries, with the rest largely Asian deposits, according to Fitch Ratings, adding that about 60 percent of all deposits - both domestic and overseas - were due to mature within three months.

Qatari bankers have expressed confidence in the state's ability and willingness to continue providing funds, pointing out that even before the crisis the public sector regularly placed deposits with Qatari banks and that the money injected so far was small compared to the state's reserves, which amount to around $340 billion.

That should easily be enough to cover the potential $35 billion in GCC claims on the Qatari banking sector estimated by Bank of America Merrill Lynch.

But analysts still expect obstacles ahead for Qatari banks. "We expect funding challenges for the Qatari banks, considering the government would still intend to continue their project plans for FIFA 2022," said Chiradeep Ghosh, banking analyst at SICO Bahrain.

Qatar is preparing to host the FIFA World Cup 2022, with banks playing an important role in helping to finance some of the $200 billion of infrastructure spending.

(Reporting By Tom Arnold and Saeed Azhar; Editing by Adrian Croft) ((Tom.Arnold@thomsonreuters.com; +97144536265; Reuters Messaging: tom.arnold.thomsonreuters.com@reuters.net))