user: The UK has pledged to take up to 20,000 refugees over the next five years.
Labour's Andy Burnham welcomed the move, but questioned whether more refugees should be accepted by the UK.
Earlier, it was announced that Royal Navy ship HMS Richmond will be deployed to help tackle people smugglers.
The warship will be deployed for two months to board and seize vessels off the coast of Libya.
The government has said it will take refugees from UN camps on the border with Syria.
But the UK will not take part in a proposed EU-wide resettlement scheme for refugees who have already arrived in Europe.
In a Commons statement, Mrs May said many refugees had been through "heart shattering" experiences and seen loved ones die.
She told MPs: "I know that honourable members and the general public are keen to know more detail on the numbers and when people are expected to arrive.
"But I must underline that the scale of the expansion needs careful and meticulous planning to ensure we get it right."
The government was "working at speed" to plan for even more arrivals in the coming weeks, she said.
In response to questioning from MPs, she added that refugees would be subject to security checks to make sure Islamic State militants were not among them.
She did not say how many refugees would arrive in the first wave, but the BBC's Daniel Sandford said he understood the government was aiming to take about 400 people a month.
The UN was able to send people quickly, but security checks by the UK authorities would take time, he added.
Shadow home secretary Mr Burnham said with winter approaching and temperatures dropping, there needed to be an "urgent solution" to stop more refugees risking dangerous voyages by boat to Europe.
He welcomed last week's announcement the UK would accept 20,000 further refugees, but stressed there needed to be "clarity on headline figures".
He also queried whether the government's decision not to take any refugees from Europe was sustainable "from a moral and a practical point of view".
The SNP's Joanna Cherry QC said her party believes "the UK Government is not doing enough in the face of the extraordinary humanitarian crisis".
The home secretary said she would update Parliament on the numbers in due course.
Europe has been struggling to deal with a huge influx of refugees.
Most are fleeing the conflict in Syria but large numbers are also escaping from violence and poverty in Afghanistan, Eritrea and Kosovo.
In the latest developments, Croatia says it will allow migrants to travel on to northern Europe - opening up a new route a day after Hungary sealed its border with Serbia.
Several other countries have tightened their border controls, including Germany, Austria and the Netherlands.

Sum: The first Syrian refugees to be taken in under the government's expanded resettlement scheme will arrive in Britain "in the coming days", Home Secretary Theresa May has said.


Article: Liverpool-based Merseycare and Stanford University have been in talks on how the technology could work.
The aim is to have the prototype ready by June with the first patients being monitored in January.
There were 6,122 suicides in the UK in 2014 - a 2% decrease on the year before.
The app would allow clinicians to provide round-the-clock observations on people who they fear may be considering suicide.
It would work by monitoring all digital communications by a patient - emails, social media, even phone calls - and spot potential dangers.
Three quarters of suicides are in men.
If for instance someone was tracked as being at a well-known suicide hotspot, or missed an appointment, or even told a friend they were feeling suicidal, the app would alert clinicians who would then be able to contact the person and provide appropriate support.
All patients would have to voluntarily submit to being monitored.
Dr David Fearnley, medical director at Merseycare, said: "The potential is incredible."
He added: "We think we can anticipate people who may be likely to harm themselves with greater accuracy than we currently do, and therefore be able to do something about it and save their lives."
Last year, Merseycare committed itself to a zero suicide policy by 2020, meaning they hope to end all suicides of service users.
The initiative requires a new approach across the trust, from staff training to greater patient involvement.
The development of the app is part of that process, and is based on a belief that people are often more open with their friends and relatives than they are with clinicians.
"This is an opportunity to exploit technology in a way we've never been able to before in health, by providing very powerful, decision-making, statistical support to clinicians in real time for the people who are most at risk," added Dr Fearnley.
The development of the app builds on work that five NHS trusts and US hospitals are already engaged in.
Their collaboration has created technology that is already scanning all the data being inputted in the trusts, digitising and analysing it and telling medics - within hours - where danger signs, such as falls or medication problems, are emerging.
Merseycare and Stanford are aiming for patients to start using the app in January 2017; its success will then be evaluated by outside experts over the following three years.
++++++++++
Summarize:

assistant: An NHS mental health trust is working with US researchers to develop an app that may stop people from killing themselves.