It was very important that Russia should show the attacks were not on moderate opponents of President Assad, he told the UN Security Council.
Russian defence officials say their aircraft targeted IS.
But an unnamed US official told Reuters that so far they did not seem to be targeting IS-held territory.
Russia's strikes reportedly hit rebel-controlled areas of Homs and Hama provinces, causing casualties.
Mr Hammond told the UN Security Council that it was "very important" that Russia was able to confirm that the strikes were directed at IS - also referred to as ISIL -and al-Qaeda affiliated targets only and not at moderate opponents of President Bashar al-Assad.
He said: "Actions in support of the [Syrian] regime are incompatible with the effective prosecution of the war against ISIL in Syria."
Meanwhile, Prime Minister David Cameron said if Russia's action was in defence of President Bashar al-Assad then that would be a "retrograde step".
Speaking on a visit to Jamaica he said: "We'll need to look very carefully at the reports and exactly what has happened.
"I have a clear view, which is that if this is part of international action against ISIL and that appalling terrorist death cult outfit, then that is all to the good."
Earlier, Mr Hammond said the UK would continue to bomb the extremist group Islamic State for "as long as it takes".
He told the UN General Assembly the people of Syria were facing the "twin evils" of IS and President Assad's "murderous regime".
He also spoke about the need to offer sanctuary to Syrian refugees.
Two years ago the House of Commons voted against UK military action in Syria, but last September it approved British participation in air strikes against IS targets in Iraq only.
Earlier this the month, Prime Minister David Cameron revealed the UK had carried out its first RAF drone attack against one of its own citizens, when it killed Cardiff-born Reyaad Khan, 21, in Syria.
Delivering the UK's national speech to the General Assembly, Mr Hammond described Iraq and Syria as the "crucible of human civilisation" where current events meant "our collective values and our will to act are being most immediately challenged".
He told world leaders at the gathering in New York that they must work together to "crush" IS - which took control of large parts of Iraq and Syria in 2014.
"We share a responsibility to act to end the bloody civil war and create an inclusive political process, and to work together to crush IS and banish its ideology from the face of the earth," he said.
"The UK will continue to be a leading member of the international coalition against Isil, including carrying out more air strikes in Iraq than any other country except the US, for as long as it takes to prevail in what will ultimately be a generational struggle against the Islamist extremist ideology that drives it."
Mr Hammond went on to praise the "extraordinary generosity" of Turkey, Lebanon and Jordan for their humanitarian efforts taking in Syrian refugees.
"It is incumbent upon all of us to support them as they bear that burden; to ensure that the UN appeals for Syria are fully funded.
"And I am proud that the UK is making the second largest contribution of any country to the humanitarian mission in the region."
The UK has pledged to take in 20,000 refugees from camps bordering Syria by 2020.
Foreign Secretary Philip Hammond has said Russia must confirm its air strikes in Syria were aimed at Islamic State or al-Qaeda affiliates.