MOSCOW (Reuters) - Moscow sees a growing chance to reach international agreement on fighting terrorism in Syria and resolving a conflict which has killed a quarter of a million people, a Russian diplomatic source said on Wednesday.

Diplomacy has so far failed to find a solution to the crisis, now in its fifth year, with international powers supporting rival sides and unable to overcome their differences over the fate of Syrian President Bashar al-Assad.

With Assad facing increasing pressure from Islamic State and Western-backed rebels, Moscow has stepped up support for its long-time ally at the same time as it pushes a new diplomatic offensive on Syria.

It has increased arms supplies to the Syrian army and increased its military presence inside Syria, drawing warnings from Western nations - which oppose Assad - that it was destabilizing the situation further.

It is not clear what agreement could be reached on the main sticking points in the conflict, but the Russian diplomatic source said the growing threat posed by Islamic State was driving new international efforts for a deal

"Moscow now has an optimistic view of chances for a settlement on Syria and uniting efforts to combat Islamic State," the source said.

The drive may culminate later this month when world leaders meet in New York at the annual U.N. General Assembly summit.

Syria is also the key theme in Russian President Vladimir Putin's talks this week with Israeli Prime Minister Benjamin Netanyahu, Palestinian President Mahmoud Abbas and Turkey's Tayyip Erdogan.

Moscow and Washington restarted talks between their defense officials on Syria last week after a long pause in any such contacts amid chilly bilateral ties over another conflict - Ukraine.

(Reporting by Gabriela Baczynska; Editing by Dominic Evans)