The launch ended a difficult week for the veteran socialist, after a muddle on his Brexit position and the leaking of Labour's draft manifesto for the June 8 vote.
Speaking at the Chatham House international affairs think-tank in London, Corbyn said the world was "becoming more dangerous" due to war, climate change, the refugee crisis and a "grotesque level of inequality".
He also cited Trump, saying he seemed "sadly determined to add to the dangers by recklessly escalating the confrontation with North Korea, unilaterally launching missile strikes on Syria", and opposing his predecessor Barack Obama's "great achievement" of a deal with Iran on its nuclear ambitions.
"Waiting to see which way the wind blows in Washington isn't strong leadership.
"And pandering to an erratic Trump administration will not deliver stability," he added, in reference to May's "strong and stable leadership" election campaign mantra.
Corbyn chaired the Stop the War Coalition, a left-wing anti-war organisation founded in 2001.
But while Britain's international relations should be based on dialogue, he insisted he was "not a pacifist".
"I accept that military action, under international law and as a genuine last resort, is in some circumstances necessary," he said.
Armed forces minister Mike Penning said: "Jeremy Corbyn has spent a lifetime trying to disarm Britain but now he's pretending he's got what it takes to keep us safe. It's nonsense.
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