Rex Tillerson said on Tuesday that the Trump administration’s proposal to slash the state department and foreign aid budget is in part based on an expectation it will be able to resolve some of the global conflicts that have been absorbing costly diplomatic and humanitarian support.

But in a vivid display of the most urgent diplomatic challenge facing the US, Tillerson was speaking as North Korea carried out a new ballistic missile test – the first since it fired a missile over Japan in mid-September.

The secretary of state presented this rationale for the budget cut at a time when he is under fire from former US diplomats for gutting his state department amid multiple crises around the world – an allegation Tillerson denied.

Tillerson, a former ExxonMobil oil executive, has faced a rising chorus of criticism for his management of US diplomacy.

On Tuesday, the former director of the state department policy planning office, David McKean, complained that Tillerson had become fixated on restructuring the department, at the expense of substantive diplomatic work. McKean’s commentary in Politico was titled: Rex Tillerson is Fiddling with PowerPoint while the World Burns.

On the same day, the woman overseeing the department’s redesign, Maliz Beams, abruptly resigned, and two former senior US diplomats, Nicholas Burns and Ryan Crocker, warned that the budget cuts coupled with the administration’s “dismissive attitude toward our diplomats and diplomacy” threaten to dismantle the US foreign service, “just when we need it most”.

Responding to those criticisms at the Wilson Centre in Washington, Tillerson argued the current combined state department and US Agency for International Development budget of $55bn was at a historic high and was not sustainable. The administration has proposed cuts of about 31%, but Congress is resisting such draconian measures.

On Tuesday, the secretary of state said he was “offended” by suggestions that “somehow we don’t have a state department that works”.

And he offered a further rationale for the retrenchment, based on an assumption that the world would become more peaceful.

“Part of this bringing the budget numbers back down is reflective of an expectation that we’re going to have success in some of these conflict areas, getting these conflicts resolved and moving to a different place in terms of the kind of support we have to give,” Tillerson said.

However, elsewhere in Washington, reporters at the Pentagon were told on Tuesday by the top US commander in Afghanistan, Gen John Nicholson, that the US combat operations in Afghanistan, would “increase dramatically over what we have done in the past year.” Nicholson last week described the 16-year-old war as a stalemate but on Tuesday claimed it had “turned a corner” and that the momentum was “now with the Afghan security forces”.

The secretary of state defended his record after a speech on US-European relations that emphasised Nato solidarity in the face of what he called Russian “aggression”, ruling out lifting Ukraine-related sanctions until the country’s territorial integrity had been fully restored.

Tillerson said the conflict in Ukraine would not be resolved without the restoration of Ukrainian sovereignty and territorial integrity. That would entail a reversal of Russia’s annexation of Crimea and a withdrawal of its support for separatists in western Ukraine, in line with a 2014 agreement in Minsk.

“Any resolution of the war that doesn’t entail a fully independent, sovereign and territorially whole Ukraine is unacceptable,” Tillerson said. “Russia chose to violate the sovereignty of the largest country in Europe. The United States and Europe have stood shoulder to shoulder since 2014 in confronting this Russian aggression with a coordinated sanctions policy.”

Tillerson added: “Let me clear. Minsk-related sanctions will remain in place until Russia reverses the actions that triggered them.”

The secretary of state’s tough language on Russia appeared to be aimed at reassuring Nato allies before a planned European trip next week, when he will visit Brussels, Stockholm, Vienna and Paris.

He also had a message on Brexit, vowing that the US was committed to maintaining its “special relationship” with the UK and a “strong relationship” with the EU. He urged both parties to resolve their divorce “swiftly and without unnecessary acrimony”.