LONDON, June 13 (Reuters) - Middle East envoy Tony Blair said on Sunday he hoped to see movement in the next few days on easing the Israeli blockade of the Gaza Strip.

Israeli Prime Minister Benjamin Netanyahu, under rising pressure to ease the embargo since a deadly raid on a Turkish-backed aid ship heading to Gaza last month, held talks on the issue with Blair on Friday.

Asked when supplies could begin getting through to Gaza, Blair told the BBC: I think it's got to be pretty soon.

As fast as the next few days I hope we can get significant movement on this because otherwise I think the pressure will build up, he said.

As Benjamin Netanyahu has quite rightly said today, there is a way to distinguish between the security aspect and the daily life aspect. And if we keep that distinction in our mind then I think we will get the right answer and we can start that quickly, he said.

The former British prime minister said the Palestinian authorities and the European Union, as well as Israel, could play a role in policing the flow of goods into Gaza.

There are all sorts of different ways that you can help police this material, the main thing is to make whatever policing system you have effective, said Blair, the envoy for the Quartet of international powers -- the United States, European Union, United Nations and Russia -- seeking peace in the region.

Arab League chief Amr Moussa visited the Gaza Strip on Sunday, the highest Arab official to do so since its seizure by Hamas Islamists in 2007, and called for an end to Israel's blockade of the Palestinian territory.

Israel said on Friday it wanted to enlist global support to improve the flow of civilian goods to the Gaza Strip, while ensuring weapons did not reach the territory.

Israeli soldiers shot dead nine Turkish protesters last month after being assaulted with knives and clubs when they boarded the humanitarian aid vessel to prevent it from breaching the blockade.

A variety of goods enter Gaza from neighbouring Egypt as well as from Israel, but aid groups have warned of a looming humanitarian disaster in the area home to 1.5 million Palestinians, due to Israel's restrictions on goods transiting its crossings.

Israel says the embargo it imposed when Hamas rose to power in 2006 is aimed at preventing weapons from reaching the Iranian-backed Islamists who have refused peace initiatives with Israel because they reject its right to exist.

Blair said he believed reconciliation between Hamas and Palestinian President Mahmoud Abbas's Fatah faction was possible.

For people like myself it would be far better if we were engaging with Hamas constructively. The difficulty is when Hamas are still prepared to say 'we don't give up the use of violence ...', he said.

I hope they decide they do want to be part of it (the peace process) because the door is open if they want to go through it, Blair added.