A number of international phone connections were established a little before or just after 1900:
Paris - Brussels phone line in 1886
England - France cross-Channel telephone cable in 1891
Britain - Belgium telephone service in 1903
Prior to these, the first ever international call was apparently made in 1881 (New Brunswick, Canada - Maine, USA).
With President Rutherford B. Hayes installing the White House's first telephone in 1877 and British Prime Minister William Gladstone doing likewise at 10 Downing Street in around 1884, at least two world leaders saw the potential for rapid communication early on. William McKinley (1897 - 1901) was also keen on the new gadget, being the first to use it for a US presidential campaign.
As the first transatlantic call was not possible until January 1927, these leaders would obviously not have been able to talk to each other but there were other (early) possibilities, most obviously perhaps in Europe. One or more calls between, for example, the British and French leaders during World War I seems a distinct possibility but I haven't been able to find any evidence.
Churchill and Roosevelt were phoning each other even before Churchill became Prime Minister in May 1940, but this was 50 years after the first international phone lines were laid down, and more than ten years after transatlantic calls started. There were several major events (not least World War I) during these years and thus potentially plenty of reasons for leaders to want to communicate quickly and personally.
When was the first (known) time the leaders of two countries spoke to each other, either by radiotelephone or telephone?
Note: I'm only interested in spoken communication. In countries with a monarchy, either the monarch or the prime minister, chancellor, etc. (i.e. Head of Government) would be acceptable as a 'leader' for the purposes of this question. A governor general or representative of a dominion or colony would be of secondary interest.