Following a closed-door congressional hearing, he told waiting media that he had answered all the questions put to him.
And then speaking afterwards at the White House, he added: “All of my actions were proper.”
He went on: “I did not collude with Russia, nor do I know of anyone else in the campaign who did so.”
Mr Kushner hit out at critics, saying the Trump campaign “had a better message and ran a smarter campaign and that is why he won” – adding that he has been “fully transparent in providing all requested information”.
In an 11-page written statement before his appearance at the meeting, the senior aide to the US President insisted there was no deal with “any foreign government” prior to last year’s US election.
The property developer, who is believed to be subject to an FBI investigation into Russia’s alleged role in the US election, wrote: “I did not collude, nor know of anyone else in the campaign who colluded, with any foreign government.
“I had no improper contacts. I have not relied on Russian funds to finance my business activities in the private sector.”
In his statement, Mr Kushner said he had “perhaps four contacts with Russian representatives” out of thousands of meetings during the election campaign and Mr Trump’s later transition to the presidency.
He said none “were impactful in any way to the election or particularly memorable”.
Mr Kushner, who is married to Mr Trump’s eldest daughter and fellow White House adviser Ivanka Trump, expressed his hope “this puts these matters to rest” and is “grateful for the opportunity to set the record straight”.
As he left the hearing, a protester blocked waiting reporters, shouting: “Impeach this president!”
The role of the US President’s son-in-law has come under scrutiny after Mr Trump’s son, Donald Trump Jr, released emails earlier this month showing he held discussions over an offer of Russian information to “incriminate” Democratic rival Hillary Clinton.
A subsequent meeting with a Russian lawyer, Natalia Veselnitskaya, in June 2016 was also attended by Mr Kushner and Paul Manafort, the Trump campaign chief at the time.
Alleged links between the Trump campaign and Russia – along with Moscow’s possible meddling in the US election – are currently the focus of a number of inquiries, including an investigation by special counsel Robert Mueller, an ex-FBI chief.
Mr Kushner described how Mr Trump asked him to be a point of contact for foreign officials wanting to get in touch with his campaign.
A short meeting with Russian ambassador Sergey Kislyak was among “normal” contacts with around 15 countries, Mr Kushner added.
He said he is “highly sceptical” of allegations he held two further phonecalls with Mr Kislyak last year, writing: “I do not recall any such calls with the Russian ambassador.”
Following Mr Trump’s election victory on 9 November, Mr Kushner claimed he “could not even remember the name of the Russian ambassador”.
Describing a post-election meeting in which he asked Mr Kislyak for the best method of holding “direct discussions” with Moscow, Mr Kushner wrote: “The fact that I was asking about ways to start a dialogue after election day should of course be viewed as strong evidence that I was not aware of one that existed before election day.”
He denied attempting to set up a “secret back channel” with Moscow in the wake of Mr Trump’s election, following previous claims Mr Kushner suggested using Russian diplomatic facilities for their discussions.
Mr Kushner branded the 9 June meeting a “waste of time” and insisted he was unaware Ms Veselnitskaya would be present, adding he had never met her since.
He wrote: “In looking for a polite way to leave and get back to my work, I actually emailed an assistant from the meeting after I had been there for 10-or-so minutes and wrote ‘Can u pls call me on my cell? Need excuse to get out of meeting’.”
Mr Kushner said he did not initially disclose any meetings with Russians or any other foreign government officials on a government security form because it was “prematurely submitted due to a miscommunication”.
He will appear before the House Intelligence Committee on Tuesday.
That panel is also probing Russian interference in the US election and possible links with the Trump campaign.
After 1 year of investigation with Zero evidence being found, Chuck Schumer just stated that “Democrats should blame ourselves,not Russia.”
— Donald J. Trump (@realDonaldTrump) July 24, 2017
Some US politicians have demanded answers over whether Russian social media “trolls” were connected to Mr Trump’s campaign, for which Mr Kushner oversaw digital strategy.
The US President has described the various investigations as a “witch hunt” into “phony” allegations.
Without giving proof, he said on Twitter no evidence had been found regarding Russia and said Senate Democratic leader Charles Schumer had cast blame on Democrats, not Russia, for the election loss.