Donald Trump has said he is looking forward to a second meeting with Vladimir Putin, as both leaders hit out at critics of their controversial summit in Helsinki.

A day after Mr Trump said for the first time he held the Russian leader personally responsible for Moscow’s meddling in the 2016 election, he said he was looking ahead to a second meeting to begin implementing some of the ideas they discussed in Finland.

“The summit with Russia was a great success, except with the real enemy of the people, the Fake News Media, Mr Trump wrote on Twitter.

President Trump on his thoughts on Vladimir Putin and US Russian relations

“I look forward to our second meeting so that we can start implementing some of the many things discussed, including stopping terrorism, security for Israel, nuclear proliferation, cyber attacks, trade, Ukraine, Middle East peace, North Korea and more.”

Earlier, Mr Putin had accused forces in the US of seeking to undermine the success of the two leaders first bi-lateral summit. He vowed that he and Mr Trump would regardless work to improve relations between the world’s most heavily-armed nuclear powers.

Speaking to Russian diplomats from around the world who had gathered Mr Putin said his meeting on Monday with Mr Trump had been “successful overall and led to some useful agreements”.

“Of course, let's see how events will develop further,” he said, according to Reuters.

Trump in Helsinki: Putin meeting and protests Show all 16 1 /16 Trump in Helsinki: Putin meeting and protests Trump in Helsinki: Putin meeting and protests President Trump meets with Russian President Vladimir Putin in Helsinki Reuters Trump in Helsinki: Putin meeting and protests An advert from Finnish newspaper Helsingin Sanomat is on display in Helsinki Reuters Trump in Helsinki: Putin meeting and protests President Trump in a meeting with Finnish President Sauli Niinisto AFP/Getty Trump in Helsinki: Putin meeting and protests President Trump meets with Finnish President Sauli Niinisto in Helsinki EPA Trump in Helsinki: Putin meeting and protests President Trump talks with Finnish President Sauli Niinisto in Mantyniemi, the official residence of the Finnish President EPA Trump in Helsinki: Putin meeting and protests US, Finnish and Russian flags fly in front of the Presidential Palace in Helsinki EPA Trump in Helsinki: Putin meeting and protests A protester wears a mask featuring a portrait of Russian President Vladimir Putin during the so-called "Helsinki against Trump and Putin" demonstration on July 16, 2018, in the Finnish capital Helsinki. The US and Russian leaders opened an historic summit in Helsinki on Monday, with Donald Trump promising an "extraordinary relationship" and Vladimir Putin saying it was high time to thrash out disputes around the world. / AFP PHOTO / Jonathan NACKSTRANDJONATHAN NACKSTRAND/AFP/Getty Images JONATHAN NACKSTRAND AFP/Getty Trump in Helsinki: Putin meeting and protests Vladimir Putin gifts a football to President Trump at the press conference that followed their meeting AP Trump in Helsinki: Putin meeting and protests Trump supporters hold banners during a demonstration in Helsinki AFP/Getty Trump in Helsinki: Putin meeting and protests People protest for women's reproductive rights in Helsinki's Senate Square Reuters Trump in Helsinki: Putin meeting and protests A crowd watches the motorcade transporting President Trump through Helsinki AFP/Getty Trump in Helsinki: Putin meeting and protests Russian President Putin drives through Helsinki on his way to meet with President Trump EPA Trump in Helsinki: Putin meeting and protests A man in the audience of the joint press conference holds up a sign sign that reads "NUCLEAR WEAPON BAN TREATY". REUTERS Trump in Helsinki: Putin meeting and protests A man is removed from the joint press conference in Helsinki. Security removed the man after he pulled out a sign that read "NUCLEAR WEAPON BAN TREATY". REUTERS Trump in Helsinki: Putin meeting and protests President Trump and Russia's President Putin sit for a working lunch in Finland's Presidential Palace AFP/Getty Trump in Helsinki: Putin meeting and protests President Trump meets with Russian President Vladimir Putin in Helsinki Reuters

He claimed powerful forces were trying to derail any improvement in relations between the two countries.

“We see that there are forces in the United States that are prepared to casually sacrifice Russian-US relations, to sacrifice them for their ambitions in an internal political battle in the United States,” he said.

Mr Putin did not single out any individuals by name but spoke of US politicians who put their “narrow party interests” above the best interests of their country.

Mr Putin’s speech, while high on threats, contained few new departures. Criticism of Nato enlargement has been a cornerstone of his foreign policy rhetoric, especially in later terms.

“He wasn’t signalling change,” Mark Galeotti, Senior Non-Resident Fellow at the Institute of International Relations in Prague, told The Independent. “What this was, perhaps, was a more explicit trolling of those in the US who are opposed to better relations with Russia.”

He added: “It shows that while the Russians are happy with Helsinki, they don’t really think anything has changed”

In his speech, Mr Putin warned of the dangers of Moscow and Washington failing to continue to mend ties, saying the New START strategic arms reduction treaty would expire soon unless both countries took action.

“Despite the difference in opinions [with Trump], we did agree that Russian-US relations are in an extremely unsatisfactory state,” said the Russian leader. “In many respects, they are even worse than during the Cold War.”

There has been some confusion about what precisely the two leaders discussed in a two-hour meeting, when no one else was present except for the US president’s interpreter.

After the pair’s private meeting, Russian Ministry of Defence spokesman Igor Konashenkov told the Tass news agency the department was “ready for practical implementation of the agreements in the sphere of international security reached by” the two leaders.

He went on to say the ministry was also “ready to enliven contact with the US colleagues, between our General Staffs and via other communication channels, to discuss extension of the START Treaty, cooperation in Syria, and other topical issues of military security”.

In the US, however, top US military leaders, including Defence Secretary James Mattis, have not addressed the matter.

A spokesperson for Mr Trump’s national security council told CNN the office was still “reviewing the discussion” between the leaders. The spokesperson added: “The Helsinki summit was the beginning of a process between the US and Russia to reduce tensions and advance areas of cooperation in our mutual interest.”

During the press conference in Helsinki, Mr Trump said that Mr Putin had floated the idea of members of Special Counsel Robert Mueller’s team travelling to Moscow to work with Russian investigators - something the US president described as “an incredible offer”.

On Thursday, Mr Trump’s press secretary, Sarah Huckabee Sanders, said the proposal had been been accepted.