The most senior figure in the US military has warned that the number of threats facing his country and its allies have increased over the last decade and that the armed forces must be kept strong to fight back.

In his first speech since taking over as chairman of the joint chiefs of staff, General Martin Dempsey told an audience in London on Monday that meeting the new challenges in a time of austerity would require a transformation in military thinking.

He highlighted the cyber threat as one of the most pressing, and said more needed to be done to counter the dangers online.

"Our traditional alliances and partnerships around the world are the stable platform on which we will confront these challenges," he said. "Yet it cannot be lost on us that we now face known and unknown security challenges in the context of a new fiscal reality.

"This is no small task in today's world, a world which has become more competitive as state and non-state actors have taken advantage of information technologies to become more lethal and to decentralise, network, and syndicate against us. Stated another way, the number and kinds of threats we face have increased significantly."

Dempsey, who took over from Admiral Mike Mullen in September, said that the west had to "maintain pressure on the state and non-state actors that threaten us", as well as determine how it was going to deal with countries experiencing the Arab spring, and crucially, China.

Dempsey acknowledged that the US military would have to adapt, and hinted at the financial pressures bearing down on the department of defence, which is going through an unprecedented cost-cutting phase. But he insisted the military needed to remain strong.

"We have learned much over the past ten years, and we will adjust our force structures based both on what we've learned and on new fiscal conditions," he said. "That will require us to adjust our strategic objectives and to balance capability and capacity. That is, we must have both the right tools and enough of them to credibly deter potential adversaries and to deliver on our objectives."

He added: "The time-honoured method for absorbing diminishing resources is to do less with less. That just won't work this time. The world won't co-operate."

In the future, there would have to be greater interdependence between the US and its allies – a reference, perhaps, to the frustration in Washington that some Nato countries do not pull their weight when it comes to security.

"With cost as an independent variable, we must now seek the synergies and possibilities of capabilities that are integrated and combined in innovative ways."

The general was in the UK to give the Colin Cramphorn memorial lecture at the Policy Exchange thinktank.

He will also attend a dinner tomorrow night(tues)on Tuesday to mark the role women have played in security and defence.

During his speech on Monday night, Dempsey underlined the important role women were now playing in these fields, and then told a joke about his wife, Deanie, whom he has known since he was 17.

He said that two of his classmates at school had bragged about how they had got their wives to do the housework when they were married.

"One of my friends … boasted that he had told his wife she was to do all the dishes and the house cleaning.

"He said it took a couple of days but on the third day he came home to a clean house, and the dishes were all washed and put away. The second of my friends …bragged that he had given his wife orders that she was to do all the cleaning, all the dishes, and all the cooking.

"By the third day, his house was clean, the dishes were done, and he had a delicious dinner on the table.

"They knew that I had married this young Irish girl named Deanie. I explained that soon after we were married I told her in no uncertain terms that my house was to be cleaned, the dishes scrubbed, the cooking done, and the laundry washed. And that this was to be entirely her responsibility.

"I shared with them that the first day I didn't see anything, and the second day I didn't see anything. But by the third day some of the swelling had gone down so I could see a little out of my left eye."