(CNN) Mark Zaid, an attorney for the anonymous whistleblower whose allegations about President Donald Trump's dealings with Ukraine ignited the House impeachment inquiry into the President, said Sunday he offered to have Republican lawmakers submit questions to his client directly without having to go through the committee's Democratic majority.

The whistleblower previously offered to answer lawmakers' questions under oath and in writing if they were submitted by the House Intelligence Committee as a whole. This new offer would be a direct channel of communication with the Republicans who are in the minority on that committee. Republican leadership has complained that the process is unfair and overly restrictive on their ability to question witnesses.

In a series of tweets, Zaid said Republicans on the House Intelligence Committee have sought to "expose our client's identity which could jeopardize their safety, as well as that of their family."

"Despite long standing policy of HPSCI to protect #whistleblowers, especially anonymity (btw, this was consistent with my efforts w/GOP on #Benghazi), GOP has sought to expose our client's identity which could jeopardize their safety, as well as that of their family," Zaid tweeted Sunday morning.

The lawyer continued: "We have offered to @DevinNunes, Ranking HPSCI Member, opportunity for Minority to submit through legal team written questions to WBer. Qs cannot seek identifying info, regarding which we will not provide, or otherwise be inappropriate. We will ensure timely answers. We stand ready to cooperate and ensure facts - rather than partisanship - dictates any process involving the #whistleblower."

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