The former professional comedian insisted his relationship with the former reality TV star was “very good” and that he was “sure we will have a meeting in the White House”.
But the $250m (£280m) of arms for Ukrainian forces, which are confronting Russian backed separatists, has been enmeshed in a bitter battle between the US president and his opponents over accusations that he has tried to manipulate it for underhand political reasons.
The Trump administration had in fact suspended the “Ukraine Security Assistance Initiative”, only agreeing to unblock it after rising bipartisan clamour from congress.
The ostensible reason for the hold-up was to ensure that it tallied with US interests.
The real reason, claim critics, was to pressure the Ukrainian government to target Joe Biden – the possible Democrat candidate for next year’s election – through an investigation into corruption allegations against his son.
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Members of the Trump administration have claimed that Mr Biden, then Barack Obama’s vice president, had pressured the Ukrainian authorities to drop an investigation into Burisma, an energy company operating in the country, on which his son Hunter was a board member.
The claims against Mr Biden have been denied to a number of news organisations, including The Independent, by Ukrainian and western European officials.
Three Democrat-controlled house committees – Foreign Affairs, Intelligence and Government Reform – have announced that they would investigate whether a host of ethical and legal rules have been violated.
Speaking at the annual Yalta European Strategy (YES) conference held in Kiev last weekend, Mr Zelensky said that he had been careful not to comment publicly on the issue of the American security assistance because he did not want to interfere while the decision was under review.
But the president stressed he was delighted with the decision to release the package, and also with reports that the State Department was putting together a separate aid package worth $140m.
“Now we can say we have very good relations with the US because now we will get not only $250m but [an additional] $140m. When you are waiting for $250m have the possibility to get $390m, I like this sort of relationship,” said Mr Zelensky, adding that he hoped to meet the US president soon.
“I am sure we will have a meeting in the White House, because I was invited,” he said.
But there have been claims that Mr Trump had refused to meet Mr Zelensky after his election this year, and that US officials have warned this would continue to be the case unless the Ukrainian authorities reopened the Burisma files.
The house committees’ chairs say they will scrutinise a telephone call between the US president and Mr Zelensky on 25 July, during which Mr Trump allegedly told the Ukrainian president to reopen the Biden investigation if he wanted to improve relations with the US.
They claim that Kurt Volker, the US special representative for Ukraine, was told to intercede with President Zelensky by the White House, and they are looking into the activities of Rudy Giuliani, Mr Trump’s personal lawyer.
Mr Giuliani urged Mr Zelensky soon after his election to focus on the Biden case, but the Ukrainian president is said to have refused, protesting that he did not want to get drawn into American internal politics.
This led to Mr Giuliani cancelling a trip to Kiev, saying he felt that he would be “walking into a group of people that are the enemies of our president ... in some cases the enemies of the United States”.
Mr Giuliani had subsequently met Yuriy Lutsenko, Ukraine’s then chief prosecutor, in New York, a meeting which was followed by Mr Lutsenko beginning an investigation into another Republican claim, that the Hillary Clinton campaign colluded with the previous Ukrainian government of Petro Poroshenko in an effort to obtain damaging information about Mr Trump and the Kremlin.
Mr Trump’s former campaign manager, Paul Manafort, was convicted and jailed over millions he earned from a former boss, Viktor Yanukovych – the pro-Russian leader who had to flee to Russia following the revolution six years ago – in the “Russiagate” investigation carried out by special counsel Robert Mueller.
There was also scrutiny of a Ukrainian MP, Andrii Artemenko, over an alleged deal with Moscow that drew in Michael Cohen – Trump’s former personal lawyer jailed in the Mueller inquiry – and Michael Flynn, Trump’s former national security adviser, who was also convicted by the special counsel.
Mr Giuliani had, in particular, asked for an inquiry into the “Black Ledger”, a tranche of information about Manafort which was supposedly forged.
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The Mueller investigation concluded that the documents were genuine.
It was reported that Mr Lutsenko had reopened the Biden case.
He denied this, but after facing criticism from the Trump camp, said he was preparing to pass on details of payments made by Burisma to US attorney general William Barr, in case American authorities wanted to check on whether Hunter Biden paid adequate taxes on his income.
Mr Lutsenko, however, was replaced by President Zelensky in August with Ruslan Riaboshapka.
This, according to the house committee officials as well as legal sources in Ukraine, led to a push by the Trump administration to ensure that the new chief prosecutor would pursue the Biden claims.
Mr Giuliani spoke to Andriy Yermak, a Ukrainian aide, in Madrid in the summer and acknowledged, when news of the meeting was revealed, that he had “strongly urged” the Kiev authorities to investigate whether Mr Biden had interfered in the Ukrainian legal process.
Mr Giuliani admitted that his talks with Mr Yermak had been arranged through the State Department but stressed that he had been travelling as a “private citizen” and not an official. He told the New York Times that he urged Mr Yermak to “just investigate the damn things” and left “pretty confident that they’re going to investigate it”.
Mr Biden had been among many western politicians who had criticised the Poroshenko government for doing nothing like enough to tackle corruption, after pledging it would do so in return for massive amounts of aid from Europe, the US and international organisations.
In March 2016, Mr Biden warned that $1bn in loan guarantees would be withheld by the US unless Kiev addressed the issue of graft and replaced Viktor Shokin, the prosecutor general. Mr Shokin claimed he had started an inquiry into Burisma when he was removed.
But Ukrainian prosecutors have denied to The Independent that the Burisma inquiry, part of a wider investigation into companies owned by Mykola Zlochevsky, a former minister, was even active when the prosecutor general was fired.
Vitaliy Kasko, Mr Shokin’s deputy, has produced documents which appear to show that the probe was, in fact, dormant.
Mr Shokin had faced strong criticism from a number of national and international figures.
Anders Aslund, the eminent Swedish economist and senior fellow at the think tank Atlantic Council, had stressed to The Independent when the story first surfaced that it was well known Mr Shokin had “failed to prosecute anybody of significance, protecting both the Yanukovych circle and the Poroshenko group”.
Daria Kaleniuk, the executive director of the Anti-Corruption Centre in Ukraine, wanted to point out that Mr Shokin was fired for failing to prosecute cases of corruption, not to block his crusading zeal for doing so.
The main source of the Clinton/Ukraine conspiracy in the 2016 campaign comes from a Ukrainian MP, who claims to have a recording of the head of the National Anti-Corruption Bureau of Ukraine, Artem Sytnyk, admitting to trying to help the Democrats.
Mr Sytnyk had denied the claim and the authenticity of the recording has been questioned by lawyers and the media.
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