The UK is sending around 700 troops to Cyprus in case an emergency evacuation of Lebanon is required as fighting between Israel and Hezbollah continues to escalate.
Britons have been urged to leave Lebanon but with airlines suspending flights to the country because of the escalating violence, commercial escape routes could be cut off as the situation deteriorates.
The deployment to Cyprus comes as the Government begins the first stage of its contingency plan, with the military team supported by Border Force and Foreign Office officials.
The Royal Air Force has planes and transport helicopters on standby to provide support if necessary.
Mr Healey said: “Events in the past hours and days have demonstrated how volatile this situation is, which is why our message is clear, British nationals should leave now.
“We continue to urge all sides to step back from conflict to prevent further tragic loss of life.
“Our Government is ensuring all preparations are in place to support British nationals should the situation deteriorate.
“I want to thank the British personnel who are deploying in the region for their commitment and professionalism.”
The UK already has a significant diplomatic and military presence in the region, including RAF Akrotiri in Cyprus and British ships RFA Mounts Bay and HMS Duncan, which have remained in the eastern Mediterranean over the summer.
Sir Keir Starmer urged Israel and Hezbollah to “pull back from the brink” and urged Britons to board commercial flights out of Lebanon as soon as possible.
The Prime Minister will be at the United Nations in New York on Wednesday and Thursday as world leaders attempt to prevent the fighting in Lebanon spiralling into an all-out war.
He told reporters travelling on his plane to New York: “The most important message from me this evening is to British nationals in Lebanon, to leave immediately and I just want to reinforce that.
“But it is important that we be really, really clear: now is the time to leave.
“More broadly, I am worried about the situation and I think we need to be clear we need de-escalation, we need a ceasefire, we need to pull back from the brink.
“I think that will be amongst the first topics we discuss in New York.”
The Cobra meeting chaired by Mr Healey was attended by intelligence chiefs and diplomats and provided an opportunity to test government planning.
The need for a contingency plan was underlined as more airlines cancelled flights to Lebanon on Tuesday.
Airlines in the United Arab Emirates, a key East-West travel hub, cancelled flights on Tuesday.
Long-haul carriers Emirates and Etihad cancelled flights, as did FlyDubai, the low-cost carrier.
EgyptAir also cancelled flights to Lebanon.