On the sidelines of the summit for the Organisation for the Security and Co-operation in Europe (OSCE) being held there, President Clinton will try to persuade the Russian President to find a solution to a conflict that has forced almost 200,000 from their homes.
But as he arrived in Istanbul yesterday, Mr Yeltsin insisted Russia would not pull back, and warned Western leaders not to let Chechnya dominate the summit, which begins today.
The crisis in the Caucasus looks certain to overshadow a summit where it is not on the official agenda. Mr Yeltsin, with his catalogue of ill health, rarely travels outside Russia, and he is coming here for one reason: to defend the bombardment of Chechnya.
Mr Yeltsin said: "Russia in Chechnya is acting in accordance with international civilised norms. I'm sure they will fully understand that after my speech at the summit." But he admitted that his job would "not be easy". He said that Russia would not approve any final declaration of the summit that mentioned Chechnya.
Mr Yeltsin said that the onslaught would continue until Russia has driven out the "international terrorists" who it blames for the Moscow apartment bombings that killed 300 people in September.
But even as he spoke, Russia was ignoring a new draft of the Conventional Forces in Europe Treaty, which is supposed to be signed at the summit, deploying far more tanks, planes and other weapons in the Caucasus than the treaty allows.
This is exactly the sort of situation the OSCE was formed for - its remit is to prevent conflicts in Europe and its peripheries. But Russia insists Chechnya is an internal problem, and nobody else's business.
Mr Clinton intends to use the gathering of world leaders to rally support against the Russian military campaign. But US officials yesterday acknowledged that the US could bring little pressure to bear on Russia without damaging the long-term strategy of encouraging its democracy and economic development. "We have little leverage," admitted a US official.
Mr Clinton, who was strolling around the ruins of ancient Ephesus as Mr Yeltsin faced the press yesterday, has been cast in an unexpected role. Only this summer, he was leading the Nato bombardment of Serbia during the Kosovo crisis. Now he is trying to force Russia to back down from a strategy clearly modelled on the Nato campaign.
The summit is being held in Istanbul even as the ground continues to rumble with aftershocks from Friday's terrible earthquake, and the death toll creeps up.
This was to have been Turkey's moment of triumph, playing host to a major summit a month before it hopes to be named as a candidate for membership of the EU. Instead, Turkey is desperately going on with the summit, amid warnings that Istanbul is at risk of a major quake.
The summit is also expected to cement the rapprochement that the earthquakes made possible, between Turkey and its bitter rival, Greece. But Athens said that it would have to see substantial movement on Cyprus, divided for 25 years since a Turkish invasion thwarted a coup aimed at union with Greece.
UN-sponsored talks intended to resolve the Cyprus question are scheduled to start again next month.
Bulent Ecevit, the Turkish Prime Minister, said that he would not bargain with Greece over Turkey's EU candidacy. "The important thing is that Turkish-Greek relations go forward through dialogue."Reuse content