ABUJA, Feb 20 (Matthew Tostevin - Reuters) - Middle East envoy Tony Blair said on Saturday he hoped Israelis and Palestinians would resume peace negotiations within weeks, after a break of more than a year. The former British prime minister represents the 'quartet' of Middle East negotiators, and Washington recently said he would be intensifying his work with US negotiator George Mitchell to broker talks.

'I hope we can get it going in the next weeks, but who knows,' Blair told Reuters during a visit to Nigeria. 'The Israelis want to get into negotiation, the Palestinians want to get into negotiation, the question is the terms.'

A big part of Blair's role as envoy for the United States, European Union, United Nations and Russia is helping Palestinians prepare for eventual statehood alongside Israel.

He said efforts would increase not only to strengthen the Palestinian economy and allow greater freedom of movement, but also to do more to promote the rule of law on the Palestinian side and ensure a functioning criminal justice system.

Peace talks have not resumed since Israel's war with Gaza in December 2008 and January 2009, due largely to a Palestinian demand that Israel impose a complete freeze on settlement building in the West Bank and East Jerusalem and Israel's refusal to do so.

Palestinian President Mahmoud Abbas has rejected a limited and temporary building freeze imposed by Israel late last year as insufficient, and wants assurances that renewed talks would quickly move to seeking a final deal on key issues.

Blair said proposed indirect or 'proximity talks' through Israeli and Palestinian envoys could have a role to play 'but in the end the key thing is to get to the point where the two sides are talking about the core issues and talking about them in a serious way'.

A top priority on the ground, he said, was easing Israeli restrictions on the Gaza Strip, ruled by the Islamist Hamas movement which refuses to recognise the Jewish state. The blockade has intensified the misery in the poor and crowded territory.

'We need to obviously stop attacks coming out of Gaza,' he said.

'But the single most important thing is to get this blockade of Gaza lifted or eased so that we can deal with the security issues in the proper way for Israel, but allow the people some prospect of seeing that there is a better future.'

Israeli troops shot and wounded two Palestinians in the occupied West Bank on Saturday. They appeared to have been shot as they entered Israel to seek work.

Blair was in Nigeria to support a Christian-Muslim initiative to fight the killer disease malaria. He said he hoped that would also promote understanding in a country of 140 million afflicted by sporadic religious and ethnic violence.