Nine bombers carried out a series of blasts targeting churches and hotels in the country on 21 April, killing at least 359 people – including eight Britons – and injuring more than 500.
The FCO said it issues such warnings in the case of terrorism when there are situations of extreme and imminent danger and where the threat is sufficiently specific, large-scale or endemic to affect British nationals severely.
The warning means Britons’ insurance policies may not provide cover if they travel to Sri Lanka.
There are currently around 10,000 British residents living in Sri Lanka and 8,000 UK visitors there at the moment.
The FCO has warned them to remain vigilant, keep a low profile, avoid crowded public places, large gatherings – including religious gatherings and places of worship – and any demonstrations.
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Also Britons in Sri Lanka should “avoid travelling during the night-time curfew other than to/from the airport – and keep in touch with family and friends”.
The FCO said Britons in the country who are due to leave or now want to should keep in contact with their airline, tour operator and travel insurance company in case of any new arrangements in place for customers.
It added that any Britons travelling independently should make their own arrangements to leave via commercial means, in consultation with their travel insurance company.
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If they choose to remain in Sri Lanka, then they should check that their insurance policy provides adequate cover.
The FCO said its travel advice update was a “difficult decision judged on the best possible picture” and “safety and security is its number one priority”.
On its website, it warned that terrorists were very likely to try to carry out attacks in Sri Lanka. Attacks could be indiscriminate, including in places visited by foreigners.
It said despite dozens of people being arrested in the country over the Easter Sunday atrocities, “the extent of any continued threat following the 21 April attacks remains unclear”.
The FCO added: “Some travel insurance policies may allow you to claim if you cancel a journey because of a change in our travel advice.”
Foreign Secretary Jeremy Hunt said: “Following the horrific attacks on Easter Sunday, and the ongoing Sir Lankan security operation, I have received updated advice from the Foreign Office and decided to update the travel advice to British nationals to Sri Lanka to advise against all but essential travel.
“Our hope is that it will be possible to change this when the current security operation has concluded. My first priority will always be the security of British citizens living and travelling abroad.
“We all hope the situation will return to normal very soon, and that the Sri Lankan tourism industry is able to get back on its feet following the terrorist attacks.
“We will do all we can to help the Sri Lankan authorities in the meantime.”
:: If your Sri Lanka travel plans are affected by the Foreign Office’s decision please get in touch with Sky News via:
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