Although initial tests have proved negative in both cases, more tests are being carried out and the final results may not be known until early next week.
Belgium has banned the export of all livestock after the discovery of a suspected case at a pig farm in western Flanders.
And in France, a farm in the Loire region has been put under quarantine after veterinarians said they suspected the virus might be present in flock of 24 sheep and ordered tests.
Although initial tests have proved negative in both cases, more tests are being carried out and the final results may not be known until early next week.
If either case were to be confirmed, it would dramatically strengthen fears that the current outbreak - so far confined to the United Kingdom - is likely to spread across Europe.
In Britain and Northern Ireland, the number of farms and abattoirs where the disease has been discovered is now over 50, with more being reported every day.
Ban on livestock movement
Belgium's agriculture ministry has responded to the suspected case in Flanders by imposing a total ban on the movement of farm animals throughout the country.
Agriculture Minister Jaak Gabriels also ordered a 20km (12-mile) exclusion zone to be put in place around the farm at Diksmuide, where more than 300 pigs have been slaughtered.
Both France and Belgium have already announced a cull of animals which have either been imported from the UK or have come into contact with British animals.
France had earlier become the first European Union country to ban livestock imports from the Irish Republic after foot-and-mouth was discovered in Northern Ireland on Thursday.
Paris, which has already banned British products, is also banning all livestock markets and fairs from Tuesday as a precaution.
Dublin, meanwhile, has deployed thousands of soldiers along the border with Northern Ireland in an attempt to prevent the spread of the outbreak.
Fires burn in UK
In Britain, further cases are expected to emerge next week as animals incubating the highly contagious disease develop symptoms.
But correspondents say if reports continue beyond that period, it would indicate that the situation is completely out of control.
Despite this, farmers in areas of the UK so far unaffected by the outbreak will be able to apply, from Saturday, for licences to move livestock to abattoirs.
Fires have been burning across the UK to destroy the carcasses of thousands of slaughtered livestock.
More than 40,000 animals have now been killed and government vets are trying to trace another 70,000 they think may have been infected.
Europe acts
The European Union has said there is no need to proceed to a mass vaccination programme.
Countries around Europe have, however, been steadily ratcheting up their emergency response.
Germany has ordered the immediate destruction of all sheep and goats imported from the UK in the last four weeks.
Spain has banned all livestock fairs and incinerated hundreds of British pigs.
It has also issued guidelines on cleaning and disinfecting of vehicles and the confiscation and destruction of food and waste from the UK.
Russia is imposing a blanket ban on all meat products from Britain.
The Austrian Government has advised its nationals to avoid travelling to Britain "unless absolutely necessary".