Tony Blair has urged Barack Obama to take the initiative on issues from climate change to the Israeli-Palestinian conflict as a way to heal the divisions between America and Europe.

In an interview with the Guardian during a visit to Rwanda, the former prime minister said Obama's election as US president opened up "an era of real possibility".

"I think he can say to Europe, look I'm going to champion a global deal on climate change, I'm going to take the Middle East peace process seriously, I'm going to make sure that poverty in Africa is right at the top of the agenda, I'm going to listen to your concerns and get a shared agenda with you."

But while Blair, who now serves as Middle East special envoy of the Quartet of the US, EU, Russia and the United Nations, welcomed Obama's election, he also warned that the new president would make demands on Europe and defend US interests.

"I'm not going to get into comparing presidents, because I think that would be, er, not very fruitful. But there's a tremendous possibility for Obama to reach out and create a unifying agenda," Blair said.

"People should also understand that [Obama's] agenda will encompass American interests and demands too, and once the euphoria subsides a little, as it always does in these situations, there are tough choices all round."

Blair said European governments could expect Obama to look to them for support on ensuring victory in Afghanistan, on measures to block Iran from developing nuclear weapons, and on "a set of measures on the global economic crisis that are going to work for America as well as for [Europe]".

"People have got to understand that if we really want America to be in partnership with us, and that's a good and right ambition, America will be up there making demands as well as listening to ours."

Obama faces inflated expectations, as Blair did in 1997 — in part born out of antipathy to the outgoing administration — that the president-elect's staff are already trying to dampen.

"There's enormous expectation," said Blair. "But I think he's a very smart guy and the only thing you can do in these circumstances is to try and meet the reasonable expectations."

Although unwilling to criticise President George Bush, Blair indicated that he wants to see the incoming US administration to take resolving the Israeli-Palestinian conflict more seriously.

"I personally think that one of the essential things both for the next American president and for the world is to regard this region [the Middle East], and broader than this region, as one problem because you face the same issue everywhere, which is a battle between those who want a modern and progressive future and those who are reactionary extreme," he said.

"Whether it's in Iraq or in Palestine or what's happening in all the different parts of Afghanistan or Pakistan, it's the same issue."

He questioned the established approach to the peace process which is driven, or not, by a US president backed by other foreign leaders.

He said his experience in Jerusalem and the occupied territories since he left Downing Street had made him aware of the constraints of political intervention by foreign leaders. "I do think what's very interesting about these international situations — and I found this quite shocking in a way — is how much more comprehensive my understanding of the Israel-Palestine situation is now than when I was in office," he said.

"The error in international policy, in a way, up to now on this dispute, is to think that if you get a political agreement you can then change the reality on the ground. Whereas in fact unless you are evolving the reality on the ground in a positive way you will never create the context in which a political agreement is possible, because the Israelis will never think that a Palestinian state is permissible in terms of their security and the Palestinians will never think that a state is possible because of the occupation.

"So until the Palestinians see that lifting the occupation is a genuine possibility and the Israelis see Palestinian security capability under one authority is a genuine possibility they're not actually going to make the compromises to agree."

The Palestinians say the Oslo peace process collapsed because it moved too slowly. The Israeli president and former prime minister, Shimon Peres, has said it failed because it attempted to achieve too much at once.

Blair leans toward the Israeli view, saying that what has become clear to him is that it is a mistake to pursue peace agreements on paper without the painstaking work of gradually changing the reality on the ground.

He said that had he known when he was prime minister what he knows now, it would not so much have led him to change policy as to recognise the limitations of what he could achieve as prime minister.

"More what I've learned is this: it's rather than I could have done something as British prime minister, I realised I probably couldn't because I was busy being British prime minister," he said.

Blair said that what is required is a shift away from perpetual initiatives by foreign leaders to devolving real power to international envoys committed full time.

"The interesting thing is how the international community delegates authority to make up for the limited knowledge that these leaders can have nowadays when they're dealing with a multiplicity of problems in their own domestic situation," he said.

"I think, for example, there's no way the Middle East is going to be resolved unless there are empowered senior people from the international community able to do it. Because, as I say, I now have a far better understanding of what needs to happen than I did when I was British prime minister. And yet in one sense when I was British prime minister I obviously had greater power over the situation."