The Senate Intelligence Committee is one of several congressional panels investigating the Russia matter, along with a federal criminal probe led by special counsel Robert Mueller.
After the senate meeting Kushner said Trump prevailed over his Democratic rival Hillary Clinton in November 2016 because he ran a "smarter campaign" and that to suggest otherwise "ridicules those who voted for him".
The Republican president, who calls the Russia probes politically motivated, lashed out at the investigations in Twitter messages on Monday.
In his written statement, Kushner said he first met Russian Ambassador Sergei Kislyak in Washington in April 2016 . He said he did not recall phone calls with Kislyak between April and November 2016, as reported by Reuters in May, had found no evidence of the calls in phone records and was skeptical they took place.
Kushner said he met after the election, with Sergei Gorkov, the head of Russian state-owned Vnesheconombank, because of Kislyak's insistence and because the Russian had a "direct relationship" with President Vladimir Putin.
Investigators want to hear about a June 2016 meeting involving Russian lawyer Natalia Veselnitskaya and Trump's eldest son, Donald Trump Jr.
The younger Trump has released emails that showed he welcomed the prospect of receiving damaging information from the Russian government about Clinton.
Kushner and former Trump campaign manager Paul Manafort were also at the meeting but Kushner described it as a waste of time.
He said no part of the meeting he attended "included anything about the campaign" and he had no knowledge of any documents being offered or accepted.
He said that in a December 1 meeting with Kislyak, the Russian ambassador asked if there was a secure line in Trump's transition office to facilitate a discussion with Russian generals about Syria, and Kushner replied there was not.
Kushner said he asked if the Russians had an existing communications channel at the Russian Embassy that could be used to transmit information to the transition team, but Kislyak indicated that was not possible and they agreed to follow up after the inauguration.
"Nothing else occurred. I did not suggest a 'secret back channel.' I did not suggest an ongoing secret form of communication for then or for when the administration took office," Kushner said.
Kushner did not initially disclose any meetings with Russians on forms he filed to get a government security clearance. He has since revised those forms several times.
- AAP