David Cameron has said "detailed plans" are being made for an international mission to rescue the 20,000 to 30,000 Yazidis stranded in the mountains of northern Iraq.
The Prime Minister said Britain would "play a role" in rescuing ethnic minority Kurds trapped on Mount Sinjar by Islamic State (IS) fighters .
Speaking after a Cobra meeting following a family holiday in Portugal, Mr Cameron stressed it would be a "humanitarian operation".
He said there was no need to recall Parliament to discuss it.
The UK has stepped up its aid drops and is sending a "small number" of RAF Chinook helicopters to the region. It has already sent RAF Tornado jets equipped with sophisticated surveillance equipment to gather intelligence.
Asked about calls for the UK to follow France in arming Kurdish fighters being out-gunned by IS, or to join the US in airstrikes, Mr Cameron said the "desperate humanitarian situation" needed to be dealt with first.
However, a growing number of MPs have told Sky News it is time for the UK to go further.
Sky's Political Correspondent Sophy Ridge said of the 23 MPs she had spoken to, 18 would support military intervention and many urged Mr Cameron to recall Parliament.
Conservative MP Nick de Bois said: "Whether you support airstrikes or not, and they should be on the table for urgent consideration, Parliament has both the moral obligation and a duty to our constituents to examine and advise the Government on whether we should take that step.
"Every day matters in this humanitarian crisis and that's why we should be recalled."
British commanders with experience in Iraq have also urged the Prime Minister to consider military action, with Colonel Tim Collins warning the ancient civilisations in Iraq could be "extinguished".
Col Collins claimed the Government had "left for lunch" on the issue, and accused politicians of refusing to accept the "moral responsibility" to act.
A YouGov poll carried out for The Times suggests support for the British bombing of militants in Iraq is now at 40%. Some 36% of those asked were opposed to the UK taking action.
After talks with Foreign Secretary Philip Hammond in London on Tuesday, Australian Prime Minister Tony Abbott indicated his country's combat forces could return to Iraq but stressed it would be to "prevent genocide" on a "fundamentally humanitarian mission".
Germany has pledged to deliver "non lethal" military aid, including armoured vehicles, helmets and night vision goggles, to the Iraqi army.
Former Conservative Defence Secretary Liam Fox also said it was time RAF jets were sent in to join US airstrikes.
Secretary of State John Kerry said the US would consider requests for further military assistance once Iraq's new prime minister-designate forms a government to unite the country.
Haider al Abadi is supported by the US, Iran, Turkey and Saudi Arabia - but Shi'ite party colleague Nuri al Maliki has refused to quit until there is a federal court ruling.