Qassem Suleimani was killed as part of a broader strategy of deterring challenges by US foes that also applies to China and Russia, the US secretary of state, Mike Pompeo, has said, further diluting the assertion that the senior Iranian general was targeted because he was plotting imminent attacks on US assets.

In his speech at Stanford University’s Hoover Institute, Pompeo made no mention of the threat of imminent attacks planned by Suleimani. It only was in response to a question that he repeated his earlier assertion that pre-empting such plots was the reason for the 3 January US drone strike on Iran’s second most powerful official.

His speech, titled The Restoration of Deterrence: The Iranian Example, focused on what he called a Trump administration strategy to establish “real deterrence” against Iran following earlier Republican and Democratic policies that encouraged Tehran’s “malign activity”.

Democratic and some Republican lawmakers have challenged the administration over the self-defence rationale supported by undisclosed intelligence over imminent attacks. US president Donald Trump has said the potential targets included four US embassies.

On Sunday, the defence secretary, Mark Esper, said he had seen no intelligence forewarning of imminent attacks on embassies.

Trump on Monday added new fuel to the controversy by saying “it really doesn’t matter” whether Suleimani posed an imminent threat.

Pompeo said there was “a bigger strategy” behind the killing of Suleimani, the commander of al-Quds, Iran’s elite foreign espionage and paramilitary force.

“President Trump and those of us in his national security team are re-establishing deterrence, real deterrence, against the Islamic Republic of Iran,” he said. “Your adversary must understand not only that you have the capacity to impose cost but that you’re in fact willing to do so,” Pompeo said, adding that the 2015 Iranian nuclear deal from which Trump withdrew in 2018 had emboldened Tehran.

“America now enjoys the greatest position of strength regarding Iran we’ve ever been in,” he said, pointing to the damage done to the Iranian economy by US sanctions that Trump re-imposed following his withdrawal from the nuclear deal.

“The importance of deterrence isn’t confined to Iran,” Pompeo said. “In all cases, we must deter foes to defend freedom. That’s the whole point of president Trump’s work to make our military the strongest it’s ever been.”

He cited the resumption of lethal military aid to Ukraine for defence against Russia-backed separatists, Trump’s withdrawal from an arms control accord with Moscow and tests of a new US intermediate-range cruise missile.

Pompeo also pointed to increased US naval exercises in the South China Sea in response to China’s militarisation of disputed islands and Trump’s imposition of tariffs on Chinese imports as aspects of the administration’s deterrence strategy. “We’re restoring credibility to deterrence,” he said.

His comments came as the Canadian prime minister, Justin Trudeau, said victims of an Iran-downed jetliner would still be alive if not for a recent escalation of tensions partly triggered by the US.

“I think if there were no tensions, if there was no escalation recently in the region, those Canadians would be right now home with their families,” Trudeau said in an interview with Global television, according to a transcript. He added that the international community had been “very, very clear about needing to have a non-nuclear Iran” but also in “managing the tensions in the region that are brought about by US actions as well”.

The Ukraine International Airlines Boeing 737-800 was shot down by a missile shortly after taking off from Tehran before dawn last Wednesday, killing all 176 on board, including 57 Canadians.

Longstanding US-Iran tensions have soared since missiles fired from a US drone killed Suleimani near Baghdad’s airport. Iran responded with a barrage of missiles at two US bases in Iraq, inflicting no casualties in what was seen as an attempt to prevent a spiral of escalation.

But hours later, an Iranian Revolutionary Guard unit mistakenly shot down the Ukrainian passenger jet, in what Iranian president Hassan Rouhani called a “human error”.

Trudeau also said he would have “obviously” liked a heads-up from Washington about the drone strike on Suleimani, but did not receive one. “The US makes its determinations. We attempt to work as an international community on big issues. But sometimes countries take actions without informing their allies.”