Britain is to offer another two Typhoon warplanes to patrol the skies of eastern Europe amid continuing tensions with Russia over Ukraine, David Cameron has said.

The RAF has already sent four Typhoons to join Nato's air policing mission over its Baltic member countries of Estonia, Latvia and Lithuania, and the Prime Minister made clear that Britain is ready to do more to reassure the former Soviet states that they are covered by the protective umbrella of the alliance, including extending the provision of Sentry surveillance aircraft and air-to-air refuelling.

Mr Cameron told the House of Commons Liaison Committee that Britain must prepare itself for a "very difficult long-term relationship with Russia" if Vladimir Putin does not back down from his stance on Ukraine, which has seen the Kremlin annexe the Crimean peninsula and offer support to separatist forces in the east of the country.

The PM told the committee: "We are not talking about deploying armed forces to Ukraine or anything like that. It is about making sure that we can fulfil our Nato obligations.

"We have already deployed four Typhoon aircraft to bolster the Baltic air policing mission over Estonia, Latvia and Lithuania. We are going to be offering an additional two Typhoons to that deployment."

The four Typhoons were deployed in May when Nato boosted its regular Baltic operations, under Polish leadership, in response to the Ukraine crisis. If the offer of an additional two jets is accepted, it is envisaged that the UK would take over the lead of the operation from September.

The UK is also ready to extend the operation of its Sentry surveillance aircraft in the area until the end of this year and to consider supplying air-to-air refuelling capacity, the PM indicated.

And he said: "UK personnel will participate in enhanced Nato exercises scheduled over the coming months in the Baltic states. And we are developing a range of packages to help give planning and support and other advice to our Nato allies.

"I think it is very important to give reassurance to our eastern members at this time, and to step up to the plate and make sure Britain plays its part, and we will."

Mr Cameron said that it was important for Nato to send a "clear and unambiguous message that it believes in collective security, it is a defensive alliance and reassures its eastern members".

He said that the three Baltic states have sizeable Russian minorities and have past experience of "pretty aggressive" measures from Moscow on trade and other areas in an effort to exert influence on them.

"Nato has a collective security guarantee," said Mr Cameron. "All members of Nato have that guarantee and the Latvians, Lithuanians and Estonians know they have that cloak of security around them, and I think Russia knows that too."

Mr Cameron was speaking shortly after Foreign Secretary William Hague told MPs that some pro-Russian insurgents in the east of Ukraine appear to be special forces sent by the Kremlin.

Separatists in Donetsk have declared an independent state and asked to join Russia, following referendums in the region and neighbouring Luhansk which produced majorities wanting to leave Ukraine.

The EU, which dismissed the votes as "illegitimate and illegal" , has responded to the latest developments in Ukraine by widening existing travel bans and asset freezes to a further 13 individuals as well as two firms based in Crimea, which was effectively annexed by Moscow.

After visiting Ukraine last week and attending a meeting of European foreign ministers yesterday, Mr Hague told the Commons: "In two of Ukraine's 25 regions, namely Donetsk and Luhansk in the south and east of the country, the situation has deteriorated markedly over the last two weeks.

"A constant barrage of propaganda by the Russian media and a steadily mounting death toll are contributing to an atmosphere of fear, uncertainty and division.

"So-called pro-Russian separatists led by people who by their training, equipment and behaviour give every appearance of sometimes being Russian special forces have continued to seize and occupy government buildings in the south and east of Ukraine, using many of the same tactics that were deployed in Crimea."

Mr Hague insisted that the "doors to diplomacy" remain open for Russia.

But Mr Cameron warned senior MPs on the Liaison Committee: "We have got to recognise that if this continues we have to prepare for a very difficult long-term relationship with Russia.

"I have tried to build a good relationship with Putin and enhance Anglo-Russian relations. I would like to see that happen.

"But if this continues, that is not going to be possible. We have got to make that clear to Russia and I have done in conversations with Putin."

Mr Cameron added: "Europe has got to think about its energy dependence on Russia. We in the UK are not dependent in any real regard on Russian energy, but some European countries are. Some receive 80%-90% of their gas from Russia.

"We need to make some long-term changes to our energy systems within the EU and G7 to demonstrate that this sort of behaviour can't continue."

Mr Cameron said that the UK had been "clear, predictable and tough" in the imposition of phased sanctions on Russia in response to its actions in Ukraine, and "stands ready to do more if Ukraine's territorial integrity is not respected".

He made clear that the UK still regards the Crimean peninsula as part of Ukraine, despite its annexation by Russia in March.

And he insisted that Western sanctions were having an impact on Russia: "We have seen a downgrade of their economy - instead of 2.5% growth, they have 0.2% growth this year; a big flood of money out of international markets; their bonds have been relegated to a very low status.

"It's having an impact on them. We have to keep up this pressure but offer a very clear negotiated path to how these problems can be dealt with.

"The aim we should have is not to grab Ukraine like a piece on a chess board and yank it towards Europe. Ukraine should be a bridge between Europe and Russia. Ukraine needs to have a proper relationship with Russia as well as a good relationship with Europe. It's not a zero-sum game and I am not sure the Russians have understood that that is the intention."

Mr Cameron confirmed that the UK's Department for International Development has been offering "capacity building" support to the interim authorities in Kiev ahead of the presidential elections on May 25.