The Nato alliance is about decency and dependability, not just cash and contributions, Germany’s defence minister has said in a rebuke to Donald Trump over his insistence that European countries rapidly increase their defence spending.

Ursula von der Leyen told a gathering of defence ministers in Munich the alliance was about fairness in collective decision-making, and not just during military missions.

As the conference opened a study was published showing that European Nato members would have to raise their defence spending by £102bn a year to hit the 2% of GDP target set for 2024. That would require a 38% increase in spending, the International Institute for Strategic Studies said in its annual military balance report.

The failure of Washington’s European allies to get even close to that figure has infuriated the US president, who accuses them of freeloading. The US accounts for 70% of Nato states’ defence spending, the report found. It spent nearly $650bn (£506bn) in 2018, compared with around $250bn for all the European Nato members combined.

Trump’s anger over spending has fuelled concern about his commitment to the alliance. At a Nato summit in Brussels last year he made a blistering public attack on Berlin in a televised meeting with Angela Merkel.

Von der Leyen tried to defuse a potential replay of that row on Friday by insisting that calls for Germany to increase defence spending were justified. She also pointed out that the call to hit 2% had been made by Trump’s predecessor, Barack Obama, but added, pointedly: “Yes, Nato is about cash and contributions but it is also about decency and dependability.”

Tensions are also likely to surface at the conference over the unilateral style of US foreign policy. Polls before the gathering found that most French and German respondents had greater confidence in Vladimir Putin’s leadership than Trump’s.

In an index of the damage caused by Trump’s “diplomacy by tweet” approach, defence ministers met to discuss the latest stage in the fight to defeat Islamic State (Isis) in north-east Syria after his unilateral decision to withdraw the 2,000 US troops in the country.

Pat Shanahan, on his first trip abroad as the acting US defence secretary, said he foresaw a “bigger and stronger” US-led coalition combatting Isis globally as Washington pulls its troops out of Syria.

“While the time for US troops on the ground in north-east Syria winds down, the United States remains committed to our coalition’s cause, the permanent defeat of Isis, both in the Middle East and beyond,” Shanahan said in remarks to reporters.

Facebook Twitter Pinterest The acting US defence secretary, Pat Shanahan, in Afghanistan. Photograph: Robert Burns/AP

Trump’s decision, which as yet lacks a clear timetable, angered some allies, confounded US military officials and prompted Jim Mattis to resign as defence secretary. It also left a strategic question about how to secure the mainly Kurdish north-east of Syria, where Turkey wants to impose an exclusion zone.

European officials said they were given few details during the closed-door meeting in Munich and many questions remain. “We are still trying to understand how the Americans plan to withdraw,” one European official told Reuters.

The French foreign minister Jean-Yves Le Drian said it was mystery how the US said it wanted to be tough on Iran, and yet was leaving Syria in a way that will leave Iran stronger.

Republican senator Lindsey Graham told the conference the US would be asking allies to contribute forces to help stabilise areas liberated from Isis, drawing scepticism from a French diplomat who said: “Once the Americans leave we’ll be forced to leave. We aren’t going to be the patsy for the Americans.”

The differences between the EU and US also extend to whether to seek a replacement to the INF nuclear arms treaty, from which the US and Russia have withdrawn, accusing one another of violations. Germany would like a broader replacement treaty that embraces China, but the IISS pointed out that if the terms of the current treaty were imposed on China, it would have to destroy 95% of its cruise and ballistic missile arsenal.

The US was also unrepentant about its ad hoc anti-Iran summit in Warsaw this week, saying the event was not a one-off and would lead to a new, permanent anti-Iranian coalition spanning Arab states, the US and Israel. The alliance will confront Iran’s aggressive drive to build a Shia crescent and new dynamic across the Middle East, according to the US special representative on Iran, Brian Hook.

The claim will alarm European leaders further because they face a concerted joint drive by Washington and its Arab allies to crush the 2015 Iran nuclear deal and bring about a form of regime change in Tehran through economic sanctions.

Iranian aggression across the region “had done an excellent job in driving Arab states and Israel much closer together,” Hook said.