The company said operations in Europe, Middle East and Africa (EMEA) were 15% ahead, with the Americas up by 11%, although Asia Pacific continues to lag.
The 21% fall in that part of the world primarily relates to a drop off in supplying Australian mining operations as the minerals industry there shows little sign of turning around.
Angus Cockburn, chief financial officer who will take over as interim chief executive when Rupert Soames leaves at the end of this month, said China and South East Asia had performed well in the period, while a newly opened business arm in South Korea was successful in winning shipping-related contracts.
The local business, which delivers an array of generally shorter-term projects, including sporting and entertainment events and provision of power following natural disasters, was the strongest in the period with its underlying revenue said to be 11% ahead with margins at a similar level to last year. EMEA was up by 19%, Americas by 12% although Asia Pacific was down by 10%.
Mr Cockburn said the UK, Germany and Norway were showing good signs and although continental Europe was still lagging, there were a number of positives in the Middle East. He said: "The North Sea business in Norway is busier than we have seen it in a long time.
"The Middle East has been good and we have seen quite a bit of volume in Iraq supporting oil and gas and a bit of work up in Kurdistan. Also in Qatar as the infrastructure starts to build ahead of the World Cup in 2022, while Saudi continues to be strong.
"Russia, which is a big and important market for us, has had a good start. We do a lot of oil and gas and mining work in Siberia."
Mr Cockburn acknowledged the part the energy sector has played in Aggreko's performance and said: "Oil and gas is an important sector for us. If you look at the Americas, we have grown strongly again and a lot of that is oil and gas, whether that is the Gulf of Mexico or more importantly shale.
"That has been a very good market for us and one where we are providing [higher margin] gas generation. We have changed that marketplace, innovated and are winning a lot of share there."
The power projects division, which provides longer-term power generation, saw its revenue dip 3% in the period as equipment came out of Indonesia and Japan as well as military locations in areas such as Afghanistan. The company said that had been partially offset by large installations in Mozambique and Ivory Coast.
Order levels in the first quarter were 209 megawatts (MW), similar to the fourth quarter of 2013.
However, Aggreko stated it has subsequently secured more contracts which brought its year-to- date intake to 406MW.
That includes 50MW in Senegal feeding into the local grid, 170MW of short-term work to cover summer peak periods in Saudi Arabia and Oman, plus 120MW of rental equipment being put into Libya.
Mr Cockburn said: "Last year we did 725 megawatts and this year we have 406 in the bag so we are off to a very encouraging start.
"Libya is a major contract and a country that is very short of power. We see a real opportunity there in the oil and gas sector and the utility sector."
Mr Cockburn added that the company was in the latter stages of planning for its participation in the Glasgow 2014 Commonwealth Games. He said: "We are going to use more than 130 generators, have more than 100 people employed on executing the contract and it is going to be 200 kilometres of cable so it is an enormous amount of distribution."
The company has cut its net debt by £277m in the past 12 months, with the figure standing at £320m on March 31.
Shares closed up 18p, or 1.19%, at 1528p.