Britain has tried to downplay an apparent threat to pull security co-operation unless Brussels agrees to a trade deal as part of Brexit negotiations.
In her letter to European Council president Donald Tusk triggering Article 50, British Prime Minister Theresa May warned that failure to reach a comprehensive settlement would lead to a weakening in collaboration in the fight against crime and terrorism.
Critics accused May of trying to make a trade-off between security and commerce.
But Work and Pensions Secretary Damian Green said the two issues were mentioned side by side because they were "all bound up in our membership of the European Union".
"It's not a threat, I think that's the misunderstanding," he told BBC's Newsnight. "It's absolutely not a threat."
Liberal Democrat leader Tim Farron said the letter was "utterly scandalous" and a "blatant threat", while Labour's Yvette Cooper, who chairs the Home Affairs Committee, said the PM should not be using security as a "bargaining chip" in the negotiations.
Foreign Secretary Boris Johnson, writing in the Daily Telegraph, said: "It is our clear desire and intention that we should continue to play a role as one of the indispensable guarantors of peace and stability in our continent."
"We want to continue to work with our counterparts on defence co-operation, intelligence sharing, counter-terrorism, foreign policy co-ordination - and much else besides - on an intergovernmental level.
"At the same time, the PM is right to spell out her vision of a Britain outside the single market - and outside the EU legal order - but able none the less to continue the trading relationship that is so important for businesses and consumers both sides of the Channel."
In a "historic moment from which there can be no turning back", May set Britain on the path to life outside the EU when she triggered Article 50 yesterday. She immediately ran into resistance from German Chancellor Angela Merkel and the European Parliament over her goal of conducting negotiations on Britain's trade relations with Europe at the same time as talks on arrangements for Brexit.
"The United Kingdom is leaving the European Union," May told Parliament yesterday, nine months after Britain shocked investors and world leaders by unexpectedly voting to quit the bloc. "This is an historic moment from which there can be no turning back."
May now has one of the toughest jobs of any recent British leader: holding Britain together in the face of renewed Scottish independence demands, while conducting arduous talks with 27 other EU states on finance, trade, security and other complex issues.
The outcome of the negotiations will shape the future of Britain's US$2.6 trillion ($3.7t) economy, the world's fifth biggest, and determine whether London can keep its place as one of the top two global financial centres.
For the EU, already reeling from successive crises over debt and refugees, the loss of Britain is the biggest blow yet to 60 years of efforts to forge European unity in the wake of two world wars.
Its leaders say they do not want to punish Britain.
But with nationalist, anti-European Union parties on the rise across Europe, they cannot afford to give London generous terms that might encourage other member states to break away.
The views across Europe
President Francois Hollande took the triggering of Article 50 as an opportunity to talk about the future of the bloc with its remaining 27 members. "If we want to look at our future, it should be, first of all, real unity for the 27, but also with the possibility of going faster for some countries that so decide."
"We are losing a strong and important member state," Chancellor Angela Merkel said following a telephone call with British Prime Minister Theresa May. Her Vice Chancellor, Sigmar Gabriel, struck a more upbeat note on Twitter: "Let's stay friends, dear Brits!"
For Chancellor Christian Kern, one of the main issues is Britain's considerable debts with the European Union. "Considering the reported estimates of up to €60 billion ($92b) that the Britons still owe the EU, this will surely turn into a tough struggle," he said. Foreign Minister Sebastian Kurz showed more sympathy for Britain's decision to leave. "Brexit has shown that citizens' worries and concerns must be taken seriously." As Britain will no longer contribute to the EU budget, the remaining countries should consider slashing costs rather than raising everyone's dues, Kurz added.
"Now it's farewell to Britain," said Prime Minister Lars Lokke Rasmussen. "In two years, the European family goes from 28 to 27 members. That is really sad." He added that he hoped "the divorce between the EU and Britain can take place in a decent manner, and that we can keep close ties in future. That is in everyone's interest". However, he warned: "Britain's decision to leave the EU and the single market will have consequences. Rights and obligations go hand in hand."
Sweden "regrets the British decision" to leave the EU, Prime Minister Stefan Lofven says, noting Britain has been "a close and valuable partner". Lofven welcomed the "constructive tone" in British Prime Minister Theresa May's letter triggering its exit from the bloc, adding that he wants "structured and result-oriented negotiations so that [the EU], even after the exit, [has] as good and favourable relationship with Britain as possible".
The Czech Republic
Foreign Minister Lubomir Zaoralek said that Britain's continued access to the single market after Brexit was completely out of the question. "That is as if your wife says that she wants a divorce but would like to return to the family home at any given point in order to take what she wants," he said. Zaoralek warned that Britain would lose wealth and influence.
"For many people and businesses in the Netherlands, this starts a period of uncertainty," Prime Minister Mark Rutte said. The Netherlands exported €15b worth of goods to Britain in 2015 and 100,000 Dutch citizens live there. "They want clarity as soon as possible about their future ... The Government wants this too," he said.