Unless a compromise has been reached, Russia is expected to veto the motion, the second time this month it will have exercised its veto power as one of five permanent members of the council.
The other veto was on July 8 when it objected to the Srebrenica massacre of July 1995 being described as genocide, and it was the first time since 1997 that there has been more than one veto in a calendar month.
Mr McCully suggest to New Zealand reporters in New York today that on the issue of the MH17 tribunal, Russia had not just dug in its heels.
"It would be incorrect to think that the Russian position has been that they would veto anything on this topic."
Other options were explored but it did not meet the needs of the countries most affected.
"That seems to be an unbridgeable gap at the moment."
However he said nobody had ruled out going back to the council for another attempt at a compromise at a later time.
Australian Foreign Minister Julie Bishop is in New York for the meeting along with counterparts from Ukraine, the Netherlands and Belgium and another minister from Malaysia.
The death toll included 193 Dutch citizens, 43 from Malaysia, 27 Australians, 12 Indonesians, 10 British and four from Belgium.
A New Zealand resident, Robert Ayley, from Otaki was killed as was a New Zealander, Mary Menke, who had been living in Australia with her Dutch husband.
The airliner is thought to have been shot down by Russian backed militia in the Ukraine, but Russia blamed the Ukranian Government.
Russian UN ambassador Vitaly Churkin has called the motion an "attempt to create another hotbed of confrontation here that could have very far-reaching consequences for international relations."
Russia's position is that the downing of MH17 was a criminal offence and does not fall within the orbit of international peace and security issues that the council dealt with.
It proposed an alternative resolution which sought to "broaden and deepen international co-operation in the investigation" and to get the UN Secretary General involved. But that was not acceptable.
The debate will be one of the last during New Zealand's month of presidency.
Mr McCully said it was usual for foreign ministers to chair the council when a lot of foreign ministers were present.
He said he had had a "frank but constructive discussion" with Russia to see if there was ground that could be bridged between the parties.
"We fully respect the fact that the Malaysia, Netherlands and Australian Governments are making their own decisions about the sort of resolution they require to go before the council.
"They have grieving families to account to."
He was satisfied New Zealand had done all it could to explore other avenues.
New Zealand's national vote will be in favour of the motion.
The five countries behind the resolution, Netherlands, Malaysia, Australia, Belgium and Ukraine, form the Joint Investigation Team conducting a criminal investigation into the shooting while the Dutch Safety Board is conducting a technical investigation.
• To watch the debate from 7 am Thursday, go to webtv.un.org
