"We look forward to having him before the committee once we can assure that he will be able to thoroughly answer all our questions without concerns regarding the scope of executive privilege", Emily Hytha, a spokeswoman for Republican Representative Mike Conaway, who has helped oversee the committee's Trump-Russia investigation, said in a statement.
Conway's office said the committee itself - which is investigating Russian interference in the 2016 election - had chose to delay the interview with Bannon.
California Rep. Adam Schiff said Bannon's lawyer told the committee he is barred from talking about matters during the presidential transition, his time at the White House and communications with President Donald Trump since he left in August.
When Bannon appeared before the committee on January 17, he refused to answer some questions, saying he was following White House instructions.
The White House is reviewing the Democratic memo.
"Testifying before the special counsel does not obviate Mr Bannon's obligations under the subpoena issued by the committee".
Schiff said that neither Bannon nor Lewandowski had given "legitimate" reasons for refusing to appear, and that they were expected to return.
Corey Lewandowski, President Donald Trump's former campaign manager, is refusing to appear for a second time before the House Intelligence Committee, according to the panel's top Democrat, who wants him forced to appear under subpoena.
US Starting to Withdraw Forces in Iraq Following Defeat of ISIS
An Associated Press reporter at the Al-Asad base in western Iraq saw troop movements reflecting the account by contractors. Sources say coordination will continue between the US military and Iraqi forces based on conditions not yet released.
Bannon's interview has been delayed until next week.
Moscow has denied meddling in the US presidential election, and Trump denied any collusion between his associates and Moscow.
Bannon's lawyer has been negotiating with the committee and the White House about the interview's terms.
House Intelligence is one of three congressional committees investigating Russian Federation and the 2016 United States election, after USA intelligence agencies found that Russian Federation attempted to influence the campaign on Trump's behalf.
That source noted Bannon is willing to discuss "anything and everything" with special counsel Robert Mueller. The interview, according to Schiff and other lawmakers, has now been rescheduled for next week.
One of the people says Bannon plans to tell Mueller "everything" he knows.
Trump has repeatedly denied allegations concerning his campaign's ties with Russian Federation.
House Intelligence Committee Chairman Devin Nunes, R-Calif., strides to a GOP conference joined at right by Rep. Peter King, R-N.Y., also a member of the Intelligence Committee, at the Capitol in Washington, Tuesday, Feb. 6, 2018.