Jersey officials are meeting French fishermen, who have been protesting over their post-Brexit rights, in an attempt to resolve the dispute.
Two Royal Navy ships and two French vessels are patrolling near Jersey while about 60 French and Jersey boats are at the island's St Helier port.
French fishermen say their rights are unfairly restricted by licences issued by the island under a new system.
No 10 said the PM has been in contact with Jersey officials over the row.
HMS Severn, which has previously been used to shadow Russian navy warships off the English coast, can be seen from the port, sitting off about a mile from the French boats. HMS Tamar is nearby and both ships are maintaining a presence and not making any effort to intervene.
No 10 said it sent the two navy vessels to "monitor the situation", while the maritime prefecture of Manche and mer du Nord told the BBC the two French patrol vessels were on a public service mission to ensure safety.
France has threatened to cut off electricity to Jersey, the largest Channel Island and a Crown dependency, located 14 miles (22km) off France. Crown dependencies are not part of the UK, but are defended and represented internationally by the UK government.
The boats are protesting against new fishing rules - introduced last week by the Jersey government under the UK-EU Trade and Cooperation Agreement (TCA) - which require French boats to show they have a history of fishing in Jersey's waters. But it has been claimed additional requirements were added without notice.
French authorities say "new technical measures" had not been communicated to the EU, rendering them "null and void".
"It's really important that we are able to work with those fishermen to help them provide the necessary evidence so that, if required, their licences can be amended," Senator Ian Gorst, Jersey's external relations minister, told BBC News.
"As I've said, it's important that we respond to threats, but the answer to this solution is to continue to talk and diplomacy."
Jersey fisherman Loic Farnham said of his French counterparts: "They are professional fishermen, the same as we all are, we'd like to keep it all amicable so we can have access to the markets and they can carry on earning a living in our waters."
An Elysée source said France was monitoring the situation "very closely", adding that it is "currently calm and we hope that this will remain the case".
"We want to be able to return to negotiations, that we can obtain the fishing licenses provided for in the agreement."
The maritime prefecture of Manche and mer du Nord told the BBC the two French vessels, police boat Athos and patroller Themis, were not on military missions.
It said the boats' roles were to stay in French waters and to be near to the fisherman in order to ensure safety.
A European Commission spokeswoman said talks were continuing with the UK.
At the scene: 'Red flares burning bright'
By Freddie Miller, BBC Jersey political reporter
In the darkness you could see the lights from boats slowly making their way from the direction of France towards Jersey. They then all gathered outside the St Helier harbour and they stayed there for about half an hour.
At about 06:30 BST they started making their way slowly into the harbour. Flares were set off - red flares, orange flares, burning bright. French flags were being flown, there were banners talking about fishing.
Meanwhile, on the pier-side where I am, islanders had gathered - probably about 30 in total, including a couple of police officers. Jersey flags had been hung to the railings of the pier, some were waving flags.
There were also some Jersey boats in support of the French, flying both French and Jersey flags, and also a couple that were there trying to stop the French from coming into the harbour.
Amidst all of this you've got the two navy vessels in the distance - you can just see the outline shadow of them through the mist, just keeping watch of everything.
MEP Stephanie Yon-Courtin, a member of the EU fisheries committee, told BBC Radio 4's Today programme said "all retaliatory measures will be explored".
Of the threats to cut off electricity to Jersey, she said "these are only words we are not ready for war".
On Thursday morning, Prime Minister Boris Johnson confirmed that the two Royal Navy vessels would "remain in place to monitor the situation as a precautionary measure".
A statement from the Jersey government read: "Diplomatic efforts will continue to resolve the outstanding issues relating to fishing licences and to de-escalate the situation."
At the scene: 'More shock than anger'
Their boats were draped with makeshift banners - which read "en colère"- we are angry, writes BBC Europe correspondent Jean Mackenzie, who was with the fishermen as they set off from the French coast.
A handful left this small port on the Normandy coast about 02:30, to be joined by dozens more on the way to Jersey. The fishermen seemed more shocked than angry, that their access to waters they have fished in for decades is being challenged.
Under the post-Brexit trade deal, Jersey has to allow European vessels into its waters, but they now need licences - but the fishermen say the permits have come with a long list of restrictions that were never agreed.
Reacting to the French maritime minister's threat to cut off Jersey's electricity in retaliation - the fishermen were pleased.
"It's good to know our country is on our side," they said
Dimitri Rogoff, head of fisheries for the Normandy region, said the boats would not try to block St Helier and would return to France in the afternoon, AFP reported.
Labour's shadow defence secretary John Healey said the threats were "completely unreasonable" and urged the UK government to "get round the table with French colleagues and authorities in Jersey and sort this issue out".
What is the Jersey fishing row about?
French fishermen have complained about being prevented from operating in British waters because of difficulties in obtaining licences.
Under an agreement with the EU, French boat operators must show a history of fishing in the area to receive a licence for Jersey's waters. But it has been claimed additional requirements were added without notice.
Jersey has the sole power to issue the licences, and as of last week all fishing boats were required to have a licence to operate there.
On Friday, the Jersey government granted 41 permits to French fishing vessels that are equipped with technology that allows them to be located.
But the French government claimed the list of approved ships came with further demands that "were not arranged or discussed, and which we were not notified about".
Chris Le Masurier, who runs Jersey Oyster and Normandy Trader Freight, said the French fisherman were rightly upset by the situation.
He said: "I see it as very much an insult to them and they are extremely upset. The criteria that they were given was to prove they have fished in Jersey waters for 10 days. Nothing about what species were caught, nothing about if you've fished for 20 days or 30 days [and having to] prove that."
But Don Thompson, from the Jersey Fisherman's Association, said affected French crews have "had since 1 January" to comply with the new rules and "perhaps some of the boats that perhaps didn't qualify are a little bit put-out".
The threat to cut off Jersey's electricity supply - 95% of which is delivered by three underwater cables from France - was made by French Maritime Minister Annick Girardin on Tuesday.
HMS Severn and HMS Tamar, which are based in Portsmouth, are each crewed by 45 sailors and up to 50 Royal Marines.
The ships are routinely used for fisheries protection - with sailors able to board other boats for spot checks.
Update: This story has been amended to clarify the specifications of Royal Navy vessels HMS Severn and HMS Tamar.
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