By Tom Finn and William Maclean

DOHA (Reuters) - Palestinian infighting and years of an Israeli blockade could turn the impoverished Gaza Strip into an easy "launching pad" for Islamic State recruiters, Qatar's foreign minister says.

The small gas-rich Gulf state is a major backer of Hamas, the armed movement which has maintained its control over the coastal enclave for almost a decade despite conflicts with Israel and a rift with Western-backed President Mahmoud Abbas.

Foreign minister Sheikh Mohammed bin Abdulrahman al-Thani said in an interview in Doha on Saturday that a blockade imposed on Gaza's borders by Israel and Egypt had turned the territory into an "open-air prison".

"If we will leave them as they are, people from Daesh can recruit them easily. They can start operations from there easily," he told Reuters, using an Arabic acronym for the group.

"It (Gaza) can tranform also as a launching pad for extremism and for terrorism ... That's why we need to put an end to this," he said.

Cut off from trade, many of Gaza's 2 million people live in poverty and struggle to find work. Israel and Egypt have accused Hamas of being a terrorist group exploiting Gaza's suffering for its political gain - charges the group denies.

Hamas, an Islamist movement that shares the Islamic State's hostility to Israel but not their quest for a global religious war, deny the jihadists have a presence in the territory.

Pro-Islamic State social media accounts have accused Hamas of arresting their supporters in Gaza.

Qatar has no diplomatic relations with Israel and strained ties with Egypt's military-backed government, which has kept its border with the Gaza Strip largely closed since the 2013 overthrow of Islamist President Mohamed Mursi.

Doha has paid the salaries of Gaza public sector workers and built new homes for Palestinians after a 2014 war with Israel.

The Qatari donations, as well as its hosting of Hamas leader Khaled Meshaal since 2012, have buoyed Gaza's de facto Islamist rulers, irking Israel and the U.S.-backed Palestinian administration based in the occupied West Bank.

Sheikh Mohammed said that advancing Palestinian unity efforts and easing the blockades should not be "forgotten about" because of war unfolding across the Middle East.

"We believe this will be a step for having some relief for the people of Gaza. Forgetting Palestine - postponing it until later - will be much riskier," he said, referring to the Palestinian goal of creating a state in the West Bank and Gaza.

(Additional reporting by Nidal Al Mughrabi in GAZA; Editing by Noah Browning and Louise Ireland)