The UK is ready to "help out" in Iraq where refugees have fled Islamist militants, David Cameron has said.
Mr Cameron confirmed an RAF Tornado jet made surveillance flights overnight, and there were further aid drops.
It was "good news" that fewer refugees than thought remained on Mount Sinjar in northern Iraq, he said.
International Development Secretary Justine Greening said the plight of the refugees remained "desperate" but a rescue mission was now "less likely".
A US special forces mission found that thousands of Yazidi people had managed to escape from the mountainside and the few thousand that remained were in better condition than feared.
Mr Cameron said UK Chinook helicopters had arrived at a base in Cyprus, which could be used to transport personnel or rescue refugees.
'Flexible to respond'
The prime minister was speaking at the UK Disaster Response Operations Centre at Cotswold Airport in Kemble, Gloucestershire.
"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," he said.
"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.
"What our plans need to do is to make sure that we have got the assets in place to help out in the right way and that's why last night one of our Tornados was gathering information about the situation; that's why it's important our Chinooks are in place and available if needed.
"Our plans need to be flexible enough to respond to this situation."
A Downing Street statement released after a meeting of the government's emergency Cobra committee said the need for more air drops was being reviewed, but that options would be kept open in case of "further need".
The Chinooks and Tornados would stay in the area, Downing Street said.
No 10 urged newly-appointed Iraqi Prime Minister Haider al-Abadi to "establish an inclusive government as quickly as possible".
The UK would also continue to work with the Kurdish forces to ensure they had the military supplies they needed, the statement added.
The latest air drop was the fourth made by the RAF in the past week.
The US estimated that fewer than 10,000 people were fleeing militant group Islamic State (IS), which has seized large parts of northern Iraq in recent months, according to the international development secretary.
Ms Greening told BBC Breakfast that work to get supplies to those displaced by the fighting had been "absolutely critical".
She said US air strikes were working but added Britain would support a rescue mission if necessary.
"It's been a very uncertain picture. We've seen some people leaving the mountain while other people have been forced on to it," she said.
"Clearly we will need to continue our work to get all of those supplies to people who are still there over the coming days. We will make sure we do that."
Since Saturday, the UK has delivered nearly 10,000 reusable water purification containers each containing 500 litres of clean water as well as shelter kits and solar lamps.
This is paid for by the government's £8m assistance fund, set up to help those displaced in Iraq.
Labour MP Ann Clwyd, a former special envoy to Iraq under prime ministers Tony Blair and Gordon Brown, said the UK should launch an evacuation mission and called for the recall of Parliament.
She told BBC Radio 4's World at One: "There's a problem of confusion, and as an MP with a special interest in this area I'm completely confused because how do 50,000 people suddenly diminish to such a small number when there are actually very few flights that have been able to take them out?
"But what I'm most concerned about is the plight of the people still on the mountain top, whether they are one or 500, those people should be evacuated and we should know why they cannot be evacuated, what the problems are."
The Archbishop of Canterbury called for the international community to document atrocities in northern Iraq so those responsible could be brought to justice in the future.
The Most Reverend Justin Welby described human rights abuses against Christians and other minorities by IS as "off the scale of human horror".
"In a globalised world where even distant nations are our neighbour we cannot allow these atrocities to be unleashed with impunity," he said.
On Wednesday, the UN declared the situation in the country a "level three emergency", its highest level of humanitarian crisis.
Jihadists from IS are reportedly targeting Iraqi Christians and members of the Yazidi religious sect.
About 35,000 people have escaped from the mountains into Syria and on to the Kurdistan region of Iraq in the past three days, with the UN warning they need "life-saving assistance".
Some 700,000 Yazidis are believed to have been displaced.
The US air drops have focused on delivering food and water to those trapped.
American fighter jets have also continued to conduct air strikes on IS targets in northern Iraq.
Meanwhile France has said it will arm Iraq's Kurds who are already getting US military aid to fight the Islamist militants.
Iraq has been thrown into chaos by the advance of IS, which overran Iraq's second largest city, Mosul, in June.
Its fighters had taken the central city of Falluja and parts of nearby Ramadi in December 2013.
On 29 June, IS announced it had created a caliphate, or Islamic state, stretching from Aleppo in Syria to the province of Diyala in Iraq.