The statement does not specifically mention President Trump, the assessment of the U.S. intelligence community that Russia attempted to intervene in the presidential election to ensure he would win or news that Trump's national security advisor was in frequent contact with the Russian ambassador as President Obama was considering sanctions against Russia.
"This issue is not about party, but about country. The Committee will continue to follow the facts wherever they may lead," the statement said.
The Senate Intelligence Committee, on which Sen. Dianne Feinstein (D-Calif.) serves, also is investigating Russian interference in the election, and the U.S. response.
Two Republican senators have joined a number of House and Senate Democrats, including House Select Intelligence Committee member Eric Swalwell (D-Dublin) in pushing for a nonpartisan independent commission to examine the issue.
Nunes, who served on Trump's transition committee, has previously said he doesn't think an independent commission is necessary.
The statement also asked the new, Trump-appointed heads of intelligence agencies to bring documents requested by the committee directly to committee members.
"It will not be adequate to review these documents, expected to be in the thousands of pages, at the agencies. They should be delivered to the House Intelligence Committee to provide members adequate time to examine their content," it states.