The committee announced Tuesday that it demanded Manafort's presence for a public hearing after he refused to cooperate with its terms.
"Paul Manafort met this morning, by previous agreement, with the bipartisan staff of the Senate intelligence committee and answered their questions fully", Manafort's spokesman, Paul Maloni, said in a statement to CNN.
The law generally does not make it illegal for agents of foreign governments and entities to influence US policy, but requires them to register with the Justice Department.
The two men have faced particular scrutiny about attending the Trump Tower meeting because it was described in emails to Mr Trump's son, Donald Trump Jr, as being part of a Russian government effort to aid Mr Trump's presidential campaign.
Kushner, who is a top aide in Trump's White House, met Senate Intelligence Committee investigators on Monday, telling reporters afterward he had no part in any Kremlin plot.
Instead, Glenn Simpson has agreed to a private interview, according to a person familiar with the conversations.
He was interviewed Tuesday by staffers of the Senate Intelligence Committee about his campaign contacts with Russia, The New York Times reported, citing a source familiar with the discussion.
Kushner faces questions about his involvement in a June 2016 meeting with a Russian lawyer.
While Trump Jr's attorneys agreed with the committee to meet behind closed doors, Manafort's refusal to collaborate led to him being subpoenaed, which was finally dropped.
In addition, the committee was withdrawing a separate subpoena issued for the co-founder of a research firm behind a dossier of allegations about Mr Trump and his ties to Russian Federation. "Witch Hunt. Next up, 11 year old Barron Trump!"
Paul Manafort, advisor to Republican presidential candidate Donald Trump's campaign, checks the teleprompters before Trump's speech at the Mayflower Hotel April 27, 2016 in Washington, DC.
Criminal prosecutions are rare for people who fail to register as foreign agents, according to a top Justice Department official who testified Wednesday about an obscure law receiving new attention amid investigations into contacts between the Trump campaign and Russian Federation. Trump also insisted he has complete power to pardon. Democrats have voiced opposition to speculation he will not be put under oath when answering questions.
Kushner is a quiet insider who generally avoids the spotlight. "Nothing else occurred", the statement said.
Congressional inquiries and intelligence officials have been clear in stating that they don't know how to prove if the Russian attempt to interfere (which they are convinced happened) actually changed the outcome of the election, or even any votes.