Mr Johnson was accused of throwing Sir Kim, who resigned after the leak of diplomatic cables criticising Donald Trump, “under the bus” by Foreign Office minister Sir Alan Duncan.
But stronger criticisms came from MPs in the House of Commons today during an urgent question on the leak.
Shadow Foreign Office minister Liz McInnes said “the biggest villain of all is the man about to become our next Prime Minister”.
Saying Mr Johnson refused the chance to defend Sir Kim during Tuesday’s leadership debate, Ms McInnes said: “He took an active choice instead to throw our man in Washington under the bus.
“It was the most craven and despicable act of cowardice I have seen from any candidate for public office, let alone from someone running to be Prime Minister.”
Labour MP Pat McFadden added: “The response of [Boris Johnson] was an appalling abandonment of someone in the firing line.
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“Real leaders protect their people. They don’t throw them to the wolves because they can sniff a prize for themselves.
“His actions were a chilling warning of what is to come if he becomes Prime Minister.”
Criticism also came from Tory backbencher David Morris, who said: “It is incumbent on every member of parliament in this place to back up our excellent diplomats and civil servants and [Johnson] should come to the house and apologise.”
The inquiry into the leak is focusing on whether "someone within the system" was responsible.
Sir Alan Duncan said there was no evidence the dispatches from Sir Kim had been obtained through computer hacking.
Instead, he said the investigation was looking at the possibility they had been "illicitly" released by someone with access to diplomatic reports.
Sir Kim announced on Wednesday he was standing down from his posting in Washington, saying his position had become "impossible" following a barrage of abuse from President Trump.
Downing Street has refused to be drawn on whether Mrs May intends to appoint a new ambassador before she leaves office in two weeks' time.
Allies of Mr Johnson have insisted that it must be for the next Prime Minister to decide who Britain's new envoy to the US should be.
However in response to questions, Mrs May's official spokesman said only: "In terms of this particular replacement, that will take place in due course.”