Iraq's latest bloody crisis and its links to the 2003 war brought Tony Blair back into the headlines this week, along with calls for him to step down as a Middle East peace envoy – but new evidence has emerged that his private business interests in the ever-volatile region are expanding.

Aides to the former prime minister confirmed that he was actively considering opening an office in Abu Dhabi (subscription), capital of the United Arab Emirates, which is in the frontline of the struggle against political Islam. But a spokesperson denied suggestions by a leading Arab economist that he was being considered for a job advising Oman on its long-term development, after his controversial £27m consultancy project for the Kuwaiti government in recent years.

Retired diplomats and political enemies united to demand Blair be sacked as the envoy of the Quartet – the UN, US, Russia and EU – after achieving little to promote Israeli-Palestinian peace in seven years.

Blair's Middle Eastern activities cause some irritation in Whitehall, where officials say they are not always aware of what he is doing and exactly who he is representing in meetings abroad – even though he is routinely briefed by British embassies. "He moves in mysterious ways," quipped one senior figure.

"The Blair organisation is like a sort of government with different departments doing different things," an ex-employee said. "His office is run on Downing Street lines. It's like he's never not been PM."

Aides said the Abu Dhabi office would be used for managing projects in Kazakhstan and Romania. But it will give him a presence at the heart of a strategic region. The former prime minister is close to the Abu Dhabi crown prince, Mohammed bin Zayed Al Nahyan, who is often described as being obsessed by Islamists and has lobbied hard for a tough UK line against the Muslim Brotherhood. Blair already has a contract to advise Mubadala, one of Abu Dhabi's sovereign wealth funds.

Rumours are circulating in London and Cairo of plans by Blair to advise the Egyptian government under President Abdel-Fatah al-Sisi, the former field marshal who overthrew the democratically elected but unpopular Brotherhood president, Mohamed Morsi, a year ago.

Blair has visited Cairo twice this year in his Quartet role. Alastair Campbell, his former communications chief, has also visited, and confirmed that he met "officials and politicians" to discuss "perceptions in the international media about Egypt in respect of concerns that are obvious".

Morsi's removal was followed by the killings of more than 1,000 Brotherhood supporters, mass death sentences and other human rights abuses as well as the widely condemned imprisonment of three al-Jazeera journalists after an often farcical and chaotic trial this week.

Middle Eastern sources said it was likely any work by Blair on Egypt would be done on behalf of the UAE, which with Kuwait and Saudi Arabia, in backing Sisi financially and politically. "It's pretty basic fact-gathering in support of a broader project helping the Egyptians," said one consultant.

Blair's spokesperson said: "Neither Mr Blair nor his organisations are making any money out of Egypt and there is no desire to do that."

Blair has, however, recently commissioned his own"briefing document" on the Muslim Brotherhood in Egypt, in parallel with a controversial wider review for David Cameron by Britain's ambassador to Saudi Arabia, Sir John Jenkins. Aides said it was for Blair's sole use. It was not linked to the Tony Blair Faith Foundation, which researches Middle Eastern and other issues.

The UAE is running an energetic campaign highlighting the activities of the Brotherhood, using London-based advisers to bolster their demand that its activists should not be allowed to operate in the UK. "We hope that our friends will not help our enemies," one Emirati official said. The Brotherhood insists it is a peaceful organisation that abides by UK law.

Cameron spoke to Bin Zayed about Iraq, Syria and Libya this week – a reminder of close relations with a key political and commercial partner. Britain's trade with the UAE is expected to reach £12.5bn by 2015. UAE investments in the UK amounted to £40bn by the end of 2012.

In another link between Abu Dhabi and London, Bin Zayed is advised by a low-profile former British soldier called Will Tricks, who "raised a lot of eyebrows" in Whitehall, according to ex-colleagues, when he left his MI6 posting in the UAE to work for the crown prince.

His comments on the Muslim Brotherhood and support for Sisi are stronger than anything said publicly by the UK government.

"Blair is a paid employee of Abu Dhabi because of his Mubadala contract," said Christopher Davidson, a Gulf expert at Durham University. "He should not be regarded as representing UK national interests."

Chris Doyle of the Council for Arab-British Understanding, said: "Tony Blair has to decide between his Quartet role as envoy to one of the most dangerous conflicts on the planet, his burgeoning media role in pushing for intervention in Iraq and Syria and his business interests across the globe including in the Middle East. These roles are incompatible and create a huge conflict of interest."

Blair's views on political Islam are no secret. "He's always taken a fairly strong view about not tolerating Islamic extremism and gets fed up with moderates for not acting, but he has become more right-wing on this," said a former diplomat. "The problem in Iraq was that he conflated extremism with Saddam Hussein."

Even some who admit that they share Blair's view of the Brotherhood as an extremist organisation say that does not mean endorsing repressive methods to crush it, as have been used in Egypt, where it has been proscribed.

Talk of his possible role in advising Sisi has provoked speculation and criticism. "He clearly is very experienced and has a tremendous amount of contacts – so he can provide support to any vision that Egypt might like to adopt," said Samir Radwan, a former Egyptian finance minster. "But Tony Blair sometimes waffles. If he can abandon that, he can be effective. But whether his agenda will allow him to find a way out of the tension between the Muslim Brotherhood and the government, I don't know. That would be problematic – but it doesn't make it impossible.

"Sisi himself left the door open to inclusion … what the situation needs is a catalyst. Can Tony Blair play that role? If he stops waffling, maybe. The caveat to all that is that Blair's credibility is very low in Egypt. If the Egyptian government comes out and says that Mr Blair has advised us, it would not sit well in the street because of what he did in Iraq."