Short Answer
Despite the 'distraction' of World War II, Trotsky's assassination was widely reported and commented on, but the 'interest' did not last except among Trotskyists. Stalin's Soviet Union responded to Trotsky's death by condemning him with a lengthy list of his supposed crimes, and official communist parties around the world toed the line.
Elsewhere there appears to have been little in the way of official (government-level) reaction other than the US's denial of a visa for Trotsky's corpse: Trotsky was no friend of capitalist countries and large parts of Europe were already under German occupation, their exiled governments more concerned with their own plight than that of an exiled revolutionary.
Details
Even before Trotsky's death had been confirmed, the attack on him was on the front page of the New York Times on Wednesday the 21st of August, and the story was then picked up by American radio stations later the same day, announcing his death. Opinions were divided:
As columnists wrote up their reflections on his extraordinary life,
journalists from nearly every country around the globe hurried to
Mexico City to report on the murder and its consequences. Opinions
inevitably conflicted. Yet few of his detractors, at least those
outside the Comintern parties, denied that a star of great magnitude
in contemporary affairs had been extinguished.
Source: Robert Service, 'Trotsky: A Biography' (2009)
"Front Page of the New York Daily News Announcing the Death of Leon Trotsky, 22nd August 1940". Text and image source: Allposters
The New York Times, August 22, 1940. This article continues from the front page and is mostly an account of his life. Source: Timothy Hughes Rare and Early Newspapers
Reports (not always the main headline) can also be found in, for example, Cleveland News in the US, Le Matin in France and The Ottawa Journal in Canada. The US weekly [The Nation] 9 published an excerpt on Sept. 7 from an upcoming biography by Louis Fischer detailing the rivalry between Stalin and Trotsky. In it, Fischer wrote that Trotsky was
brilliant, fiery, magnetic, and a great Intellect. But he was a
Glbraltar without a hinterland, a dreadnought sailing the seas without
escort.
In Australia, The Sydney Morning Herald printed the story of Trotsky's assassination in its 22nd August edition. More interestingly, it cited A.P.P. in New York (21st Aug.) in a small paragraph under the main article, mentioning the Mexican painter Diego Rivera linking the (then) attempted assassination to Stalin and Hitler. Rivera
...alleged the hand of Stalin, directed through Hitler, was
responsible for the attempted assassination of Trotsky.
Trotsky had lived with Rivera, and the painter had helped get permission from the Mexican government for the Soviet exile to settle there. Rivera himself had been strongly advised to leave the Soviet Union in 1928 after criticizing Stalin.
In the UK, The Guardian (or Manchester Guardian as it then was - thanks to Zeus for pointing this out) reported the facts of the murder in its 22nd of August paper (although the name of the assassin was still an alias, Franck Johnson). In another newspaper,
The London Times editorial on 23 August summarized a less positive
mood at the time: ‘The murder of Leon Trotsky at Mexico City will
relieve the Kremlin of not a few anxieties and will draw few tears
from the majority of mankind.’
Source: Robert Service
Churchill, who had become Prime Minister in May 1940, is unlikley to have mourned Trotsky as he
...hated Trotsky even more than Stalin did...
Source: David North, 'In Defense of Leon Trotsky' (2010)
This is evident from a 1938 meeting with the Soviet ambassador:
“I hate Trotsky!” Winston Churchill told the Soviet Ambassador in
1938. “It’s a very good thing that Stalin has got even with him.”
and Churchill also mentioned his dislike of Trotsky in parliament in 1944.
In the Soviet Union, the official paper Pravda was unstinting in its criticism of Trotsky
The Kremlin was jubilant; Pravda announced the demise of ‘an
international spy’...Trotsky...had fought for the interests of the tsar, landlords and capitalists.... he had worked as an agent of foreign intelligence services...
Source: Robert Service
According to Service, the Pravda text was edited Stalin himself and
Official communist parties followed the line established in Moscow,
drawing up their sentiments and phrasings from the Soviet central
well.
The Kremlin, of course, denied any involvement, and the assassin (Ramón Mercader) also denied any connection to the Soviets. In Mexico, though, the 'scene' of the crime,
Trotsky’s corpse was laid out in an open coffin and the hearse was
driven slowly through the central streets of Mexico City. Although the
deceased had been a militant atheist, 200,000 people – mostly
practising Catholics – stood on the pavements to pay their respects or
out of curiosity.
Source: Robert Service
"The casket containing the body of Leon Trotsky, slain exiled Russian leader, is shown as it was carried through a crowded Mexico City Street, Aug. 22, 1940. Trotsky's body was returned to the funeral parlor as burial had not yet been arranged. (AP Photo)". Text & Image source: AP Images.
Footage of the funeral can be seen here: 1940 Trotsky Funeral (Silent).
Trotskyists, of course, honoured their fallen comrade:
Trotskyists spoke about the deceased as if he had been the greatest
man of his time. They declared that there had been nobody like him
since Lenin. They tried to amplify publicity for the cause by
conveying Trotsky’s body to the United States. The US State Department
rejected the request: the American authorities were not going to abet
mourners in spreading any kind of communism.
Source: Robert Service
The refusal to admit Trotsky's body was mentioned by the American Trotskyist James P. Cannon, in a memorial address a week after the assassination. He presented his (unsurprisingly scathing) view of the 'capitalist' reaction:
The capitalists - all kinds - fear and hate even his dead body! The
doors of our great democracy are open to many political refugees, of
course. All sorts of reactionaries; democratic scoundrels who betrayed
and deserted their people; monarchists and even fascists - they have
all been welcomed in New York harbor. But not even the dead body of
the friend of the oppressed could find asylum here!
The great and powerful democracy of Roosevelt and [Secretary of State Cordell] Hull
wouldn't let us bring his body here for the funeral.
Source: James P. Cannon, 'Leon Trotsky Memorial Address: "To the Memory of an Old Man"'
Later, in late 1941, the American State Department opposed the publication of Trotsky's biography of Stalin for political reasons:
“It [Trotsky’s Stalin] was printed by its publisher, Harper and
Brothers, but withdrawn by them prior to public sale late in 1941”,
writes Frank C. Hanighen, feature writer for La Follette’s Progressive
in the 1st May 1944 issue. “The publishers gave as the reason for
withdrawal ‘a concern for the work’s adverse effect on international
relations’ says Mrs Lombard…”
Mrs Helen Lombard, a Washington Evening Star journalist, exposed the
book’s suppression.
“One member of Congress was asked not to let the book get out of his
hands nor permit it to be examined by any other person … State
Department officials have made informal suggestions that any quotation
from the book would be harmful to Soviet-American relations…”
explained Frank Hanighen. (Reprinted from the British Socialist
Appeal, August 1944).
Only in 1946, after Britain and the United States had fallen out with
Stalin, did the book finally appear.
(my emphasis)
In Britain, Esperantist and revolutionary socialist Frank Maitland, when presenting himself to the tribunal examining conscientious objectors on 22nd of August, was asked to which party he belonged:
...he replied ‘the Fourth International of Leon Trotsky’. ‘But isn’t
Trotsky dead?’, asked a member of the tribunal. ‘Yes’, Frank shot
back, ‘but he is still the leader of our party.’
For most countries, World War II was undoubtedly a major distraction:
The attention accorded to Trotsky might have been greater if Europe
and the Far East had not been theatres of war. Armies were on the
march. Germany and Japan were pursuing their wars of territorial
expansion. The political map of the world was being redrawn almost
daily. Trotsky’s assassination was never going to keep most people’s
attention for more than a few days.
Source: Robert Service
