David Cameron has been briefed by Tony Blair in East Jerusalem on the state of the Palestinian economy and the Middle East peace talks before a meeting with Mahmoud Abbas.

Cameron has been in Israel to address its parliament, the Knesset, and meet Israeli leaders. His visit has coincided with one of the biggest rocket attacks on Israel from Gaza in more than a year.

John Kerry, the US secretary of state, is trying to broker a peace deal with a deadline set for next month. He admitted to a congressional committee on Wednesday that levels of mistrust between Palestinians and Israelis were at an all-time high. But he said he was still hopeful an outline deal could be reached.

Blair is due to make a large donation to the Labour party for its 2015 general election campaign. His meeting with Cameron on Thursday, however, was focused on the state of the Middle East talks. Blair is trying to drive forward the Initiative for the Palestinian Economy. His visit to Israel is his 114th since he was appointed as the Quartet Middle East envoy in 2007.

Cameron went for a run in the rain before attending a business delegation meeting attended by the Israeli prime minister, Binyamin Netanyahu.

Blair's mandate as representative of the Quartet – the UN, US, EU and Russia – is to promote economic growth and job creation in the West Bank and the Gaza Strip and support the institution-building agenda of the Palestinian Authority.

His economic mandate is inextricably intertwined with the peace process since issues such as road closures, communications and trade are central to the Palestinian economy. He has also been trying to enable large-scale Palestinian investments in the technology and housing sectors.

After the meeting, the former Labour prime minister gave his backing to Cameron's drive to boost economic links. He said: "The British government has actually got a great opportunity here, because it is relatively trusted by both sides, which is quite rare in this situation.

"I think we have got the right idea on relationships between a political negotiation to resolve all the difficult issues about borders and security and Jerusalem and so on, and the economic side, which is absolutely vital because if we don't build the Palestinian economy up at the same time as you are pursuing the political negotiation then a state for the Palestinians seems a dream and not a reality.

"So this is why the business side, the trade side, is absolutely vital."

Asked whether Wednesday's missile attack could knock the peace process off track, Blair said: "The strikes from Gaza just underline and illustrate the depth of the problem.

"Gaza continues to be under lockdown, with extremist groups operating and the people in a desperate situation. One thing we are going to need, medium and long term, is a completely new strategy towards Gaza.

"However, I don't think, even with these rocket attacks, that should get in the way of pursuing a political process and a political negotiation that allows, under the leadership of the US, the two sides to come together and to try and describe an outline of what the two-state solution looks like and how a Palestinian state is going to be and to operate and to function."

Speaking after the meeting, Cameron said: "I obviously listen to Tony Blair's advice, as I listen to many people's advice."

Asked if their relationship had developed into a friendship, he said: "I wouldn't say it is about friendship," adding he had never described himself as an heir to Blair. "We were very vigorous opponents. I remember facing him across the dispatch box every Wednesday at prime minister's questions.

"We come from different political parties, different political traditions and there are many things we disagreed about, but we both want a two-state solution and he has got a contribution to help bring that about by helping generate Palestinian economic growth."

Netanyahu has said that Israel has lifted movement restrictions on the West Bank and made concessions that have not been reciprocated by Abbas.

He told Cameron on Thursday: "You're going to see President Abbas soon, only a few minutes away, and unfortunately he didn't condemn the rocketing of our civilians. He condemned the fact that Israel interdicted and hit the three terrorists who fired mortars on us. That he did condemn, and that's wrong.

"We want to move to a genuine peace. To move to a genuine peace we have to be very clear on our condemnation of terror and our support for the right to defend ourselves."

On Wednesday, Kerry said that while there were still significant issues in the progress of the negotiations, they were part of the bigger picture. "You have to see those gaps in the context of the negotiations. I do believe both parties are serious and want to find a way forward."

Kerry said that despite this, neither side believed the other was serious and that the level of mistrust between them was higher than ever.

On whether or not reaching an agreement was still an option, Kerry told Congress: "I still believe it's possible … but difficult."

The Israelis and Palestinians are preparing to confront the issue of whether Israeli Arabs will be included in the next prisoner release later this month. Palestinian officials have said in recent days that they expect Israel to release Israeli Arabs in the final group of 26 prisoners due to go free on 28 March.

Under the framework agreement from last July that led to the current negotiations, Israel was to release 104 convicted terrorists in four stages. It has already released 78 prisoners.

Cameron has said of Israel's status: "Israel is and will always be the homeland for the Jewish people; that is what the state of Israel was and is all about."