DOHA, July 22 (Reuters) - Qatar said on Thursday it would give $30 million to help pay the salaries of thousands of Gaza Strip public sector workers left without a full wage package since 2013.

The donation was welcomed by Hamas, the Islamist group that dominates the enclave who said it would help ease the wage shortages - that have tested already strained relations with the U.S.-backed Palestinian Authority, based in the West Bank.

There was no immediate comment from Palestinian Authority or Israel, who have long been suspicious of Qatar's regular donations to Hamas and other Islamist groups across the region.

The emir of the wealthy Gulf state, Sheikh Tamim bin Hamad al-Thani, said the payment of 113 million riyals was meant to "alleviate suffering and financial distress", according to Qatar's state news agency, QNA.

Hamas fighters seized control of Gaza in 2007 from forces loyal to Western-backed President Mahmoud Abbas and his Palestinian Authority, triggering years of mutual distrust.

A reconciliation pact signed in 2014 by the two sides raised hopes among Hamas that its 50,000 public sector employees' wages would be taken care of via the Palestinian Authority (PA) payroll.

But the Palestinian Authority cannot afford to pay all those extra workers and international donors who support the PA budget, including the European Union, say they want an audit of workers and cutbacks to the bloated payroll, which costs more than $2 billion a year.

The Hamas-hired public servants have grown restive and in 2014 protested over their lack of payment which is partly due to a continued blockade imposed on Gaza by both Israel and Egypt.

"The July payment will be made in full immediately once the Qatari financial fund is received," Hamas' deputy finance minister, Youssef al-Kayyali said.

Qatar, which hosts the largest U.S. air base in the Middle East, has for years preserved influence with Islamist forces across the region it believes are the long-term future.

The breadth and resilience of Qatar's links to Islamist groups including Egypt's Muslim Brotherhood, which has suffered a crackdown in the aftermath of the Arab Spring, fuels suspicions in other Gulf states.

(Reporting by Sami Aboudi and Nidal al-Mughrabi; Writing by Tom Finn) ((Tom.Finn@thomsonreuters.com;))