He must be polite, because the truth is that the West does not yet want another Gulf war. He must be tough, because the West wants Iraq to pay the price of challenging it and losing.
Following the allied victory against Iraq in 1991, when Mr Ekeus was entrusted with ensuring that Iraq was deprived of its weapons of mass destruction, he became the only person other than the Secretary-General empowered to call an emergency Security Council meeting at any time.
Two weeks ago Mr Ekeus returned from five days of talks in Baghdad, where he persuaded the Iraqis to step back from the brink and accept monitoring of their future disarmament. A few days later, in his office on the 31st floor of the UN, following an all-morning briefing with the Secretary-General, his assistant tells him the Iraqi ambassador has requested a private meeting that afternoon. Would he like other people there? 'What the hell,' Mr Ekeus says, 'give him his tete-a-tete.'
Mr Ekeus is undaunted by the Iraqis. He speaks with Swedish calm about his 16 'frosty and factual talks' facing a team led by Tariq Aziz, the Deputy Prime Minister. 'It was unclear at first whether they had a mandate from Saddam himself to give me an agreement. I think they got it while I was there. My first meeting with Aziz was postponed - because he was seeing Saddam. I think that's when he got his mandate.
'Aziz is slightly different from the others in that he's a Christian. That provides at least some conduit through which we can understand each other.'
One of the early negotiators was the dreaded Hussein Kamal Majeed, Saddam's son-in-law and the head of military industry. 'He used to throw himself sidelong on the sofa in his military regalia and affect a dismissive attitude, while Aziz sat upright, nervously puffing at his cigar. Then there was the minister for higher education - the biggest liar in the cabinet after Saddam. Two years ago he lied to us straight in the face when we asked him whether Iraq had a nuclear programme.'
Mr Ekeus went to Baghdad after a crisis developed over Iraq's refusal to instal monitoring cameras at two missile test sites. But it was the wider issue he wanted to address: 'You don't threaten to go to war over cameras, not when people are dying in Somalia and Bosnia. What I did was to turn the whole thing round and start with the political principle.
'If the mission had failed, there would probably have been military action. I don't know, since it would have been up to the Security Council, but I believed there would be.'
If what he saw was indeed a more accommodating Iraq, Mr Ekeus believes there are several reasons: 'The threat of further punitive strikes. The economy is difficult. The worst-off have always had a rotten time. During the Iran-Iraq war all the money went on weapons. The change now is that the middle class is struggling.'
What the Iraqis lack is cash to rearm. Had the ban on oil exports been lifted now, without a monitoring agreement in place as the Iraqis had demanded, it would have enabled them to quickly acquire new weapons. 'If you have money you can always find people who will help you circumvent the embargo.'
Mr Ekeus knows that the face of a more compliant Iraq worries some who fear the oil ban may now be lifted within months. 'I told the Americans yesterday: 'Don't worry so much. I don't think they will comply with everything in a hurry.' '
Mr Ekeus, a lawyer, career diplomat and veteran of arms control negotiations, is 58 and works a 70-hour week. It tells in the pallor of his face, but there is a great deal of humour in the blue eyes. 'I could also sit at home and watch television in the evenings, but this is more fun.
'Iraq has been forced to accept that all weapons of mass destruction must be eliminated. All the means of producing NBC weapons must be annihilated.
'We've relied heavily on intelligence from the countries who supplied the arms. Every country has its Iraqgate. We've proceeded steadily and slowly. I think they've seen it's very hard to hide. Our contribution is to try to guarantee the truth.'