Britain and the US will maintain a flexible military presence in northern Iraq, David Cameron has said as he hailed the "good news" which prompted Washington to call off a risky military mission to rescue thousands of Iraqis stranded on Mount Sinjar.

The prime minister, who was visiting a humanitarian aid distribution centre in Gloucestershire before chairing a Whitehall Cobra meeting on Thursday, said the continued fighting in the area meant it was right to keep military "assets" in place.

But Cameron said an American-led scouting operation had found fewer refugees than had been expected on Mount Sinjar.

Amid signs that the US bombing has succeeded in beating back forces from the Islamic State (Isis), the Pentagon said the planned rescue mission had been ruled out for the moment. A small complement of special forces and US aid workers landed on Mount Sinjar to assess the situation of the Iraqi Yazidis – who for days have received air drops of food, water and medicine.

Speaking at the UK Disaster Response Operations Centre at Cotswold airport in Kemble, the prime minister said: "There does seem to be some good news and that is the American-led scouting operation has found fewer people on the mountainside than expected. Also we see that the UK aid drops have made a difference and have got through to people. It's good news that there are fewer people there and they are in better condition than expected."

But the prime minister said Britain and the US would be ready to act quickly as the focus returned to dropping humanitarian supplies. "Our plans have got to be flexible enough to help those people, working with allies like the Kurds to make sure we can help people in need. This is a complicated humanitarian mission. One of the things we are definitely going to need to do is to get more aid into the refugee camps, like the camp at Dohuk.

"It is very difficult in an area where you have got a lot of fighting taking place, you have got a lot of people moving around. So what you need to do is have plans that are flexible enough to respond to that situation. It is important to get the assets into place. That is why the Chinooks are there. That's why our Tornados are there."

The prime minister spoke out after Washington announced overnight that a planned rescue had been called off. Rear Admiral John Kirby, the Pentagon press secretary, said late on Wednesday: "An evacuation mission is far less likely."

The decision to call off the rescue mission came as the White House declared the mission to target Isis positions in the area with four air strikes since Saturday a success. "The president's decisive decisions in the immediate wake of the crisis kept people alive and broke the siege of the mountain," a White House official said.

The prime minister had said on Wednesday that Britain planned to join the rescue mission to relieve the "desperate humanitarian" situation on the mountain. RAF Chinook helicopters were deployed to the region to help with the operation.

But Justine Greening, the international development secretary, endorsed the view in Washington that the condition of the refugees was better than expected.

Greening told the Today programme on BBC Radio 4 on Thursday: "It has been difficult to get the exact facts of what is happening on the ground, not least because we have seen people coming on to the mountain whilst at the same time others are able to leave the mountain.

"The US have reported overnight from their surveillance efforts that they think there are now fewer people left on the mountain and that those who are there are perhaps in a better state than we might have feared, which is good news. But clearly we need to continue doing the air drops we have been doing – the UK, along with the US. We have now seven, getting vital supplies like water in our case. The US has very much majored on getting food to them."

But Greening said many people left on the mountain were in "desperate straits". She said: "When you see the ones that have come off the mountain – 10,000 have gone to a camp just over the border in Syria that the International Rescue Committee are building up – they have walked for 14 miles in searing temperatures of possibly up to 50C. So they are very dehydrated, very malnourished. They need a huge amount of medical attention, so we will continue to work to help the people on the mountain."

British sources said the US air strikes had been successful in beating back Isis forces. One source said: "Barack Obama is going to do very well out of that. You are going to see advances. Stuff is really beginning to arrive."

The focus will now switch to the provision of humanitarian aid to the refugees and ammunition to the Kurdish forces fighting Isis. An emergency meeting of EU foreign ministers in Brussels on Friday is expected to approve the provision of arms to the Kurds and to agree a greater coordination of EU humanitarian relief.

Cameron spoke on Wednesday evening to François Hollande of France, the newly elected Turkish president and outgoing prime minister, Recep Tayyip Erdoğan, and Masoud Barzani, president of the Kurdistan regional government.

A Downing Street spokesman said of the call with Hollande: "On Iraq, both leaders agreed on the need to help the Kurdistan regional government tackle the threat posed by Isil [Isis], and to scale up the level of humanitarian support. They agreed that the EU could do more to provide aid and that this should be addressed at this Friday's foreign affairs council."

The logistical complexity of removing the Yazidis by air appears to be significant. While C-130 cargo planes can land on rugged terrain, the number of civilians on the mountain would necessitate numerous runs. On Monday a senior US army officer, Lieutenant General William Mayville of the Joint Staff, said the military had yet to finish devising a plan for an evacuation.