The top Republican and Democrat on the Senate Judiciary Committee have said President Donald Trump's son-in-law has not been fully forthcoming with the panel's probe into Russian election interference.

Senate Judiciary chairman Chuck Grassley and Democratic Senator Dianne Feinstein sent a letter to Jared Kushner's lawyer on Thursday saying the collection of documents he has provided the committee is "incomplete", and asking him to provide e-mails sent to him involving WikiLeaks and a "Russian backdoor overture and dinner invite".

The committee gave Mr Kushner a November 27 deadline to provide the additional documents, including the e-mails and Mr Kushner's security clearance form that originally omitted certain contacts with Russian officials.

The request is part of the panel's probe into the Russian election meddling and whether the Trump campaign was involved.

They have received documents from other campaign officials that were copied to or forwarded to Mr Kushner, but which he did not produce

The Judiciary committee is one of three congressional committees looking into the issue, along with the Senate and House intelligence panels.

The committees have separately requested and received thousands of documents from people associated with the Trump campaign, and have interviewed dozens of individuals. Department of Justice special counsel Robert Mueller is also looking into the meddling.

The senators noted they have received documents from other campaign officials that were copied to or forwarded to Mr Kushner, but which he did not produce. Those include "September 2016 e-mail communications to Mr Kushner concerning WikiLeaks".

Mr Trump's eldest son, Trump Jr, corresponded with WikiLeaks that month and, according to The Atlantic, sent an email to several Trump campaign advisers to tell them about it.

Mr Grassley and Ms Feinstein wrote that other parties have produced documents concerning a "Russian backdoor overture and dinner invite" that Mr Kushner forwarded but has not given to the committee. It is unclear what overture and dinner invite they are referring to.

The senators are also asking Mr Kushner for correspondence with former national security adviser Michael Flynn, who is a subject of an investigation by special counsel Robert Mueller.

Abbe Lowell, Mr Kushner's lawyer, said in a statement that Mr Kushner has been responsive to all requests.

"We provided the Judiciary Committee with all relevant documents that had to do with Mr Kushner's calls, contacts or meetings with Russians during the campaign and transition, which was the request," Mr Lowell said.

"We also informed the committee we will be open to responding to any additional requests and that we will continue to work with White House Counsel for any responsive documents from after the inauguration."

The letter comes as the Judiciary Committee's investigation has stalled amid partisan disputes. The new request is a sign that the panel is still moving forward with its probe into the Russian interference and whether Mr Trump's campaign was involved.

In the letter to Mr Kushner, the senators noted they had asked him to provide documents to, from, or copied to him "relating to" certain individuals of interest to investigators, but Mr Kushner responded that no e-mails had been found in which those individuals were sent e-mails, received e-mails, or were copied on them.

"If, as you suggest, Mr Kushner was unaware of, for example, any attempts at Russian interference in the 2016 presidential election, then presumably there would be few communications concerning many of the persons identified in our second request, and the corresponding burden of searching would be small," the senators wrote.

The committee also asked for the additional documents related to Mr Flynn, detailing a long list of search terms, and rebuffed Mr Kushner's lawyer's arguments that his security clearance is confidential and unavailable because it has been submitted to the FBI for review.

The Senate and House intelligence committees interviewed Mr Kushner in July. The Judiciary panel has also sought an interview with Mr Kushner, but his lawyers offered to make the transcripts available from the other interviews instead, according to the letter. The senators say those panels have not provided them with those transcripts, and ask Mr Lowell to secure that access.

Then "we will consider whether the transcript satisfies the needs of our investigation," Mr Grassley and Ms Feinstein wrote.